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AP Calculus AB Flashcards: Integrating Using Substitution

Study Integrating Using Substitution in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Integrating Using Substitution, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Integrating Using Substitution

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QUESTION

What substitution simplifies the integral of $(2x + 1)^5$ ?

Tap or drag to reveal answer

ANSWER

$u = 2x + 1$ . Let $u = 2x + 1$ to transform $(2x + 1)^5$ into $u^5$ for easier integration.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: What substitution simplifies the integral of $(2x + 1)^5$ ?

Answer: $u = 2x + 1$ . Let $u = 2x + 1$ to transform $(2x + 1)^5$ into $u^5$ for easier integration.

Flashcard 2: What is the substitution for $u$ if $du = -\text{sin } x \, dx$ ?

Answer: $u = \text{cos } x$ . Since $\frac{d}{dx}(\cos x) = -\sin x$ , if $du = -\sin x dx$ , then $u = \cos x$ .

Flashcard 3: What is the integral of $\frac{1}{u} \, du$ ?

Answer: $\text{ln } |u| + C$ . The antiderivative of $\frac{1}{u}$ is $\ln|u|$ plus the constant of integration.

Flashcard 4: Determine $du$ for $u = \text{sin } x$ in substitution.

Answer: $du = \text{cos } x \, dx$ . The derivative of $u = \sin x$ is $\cos x$ , so $du = \cos x dx$ .

Flashcard 5: Determine $du$ if $u = \text{tan } x$ in substitution.

Answer: $du = \text{sec}^2 x \, dx$ . The derivative of $u = \tan x$ is $\sec^2 x$ , so $du = \sec^2 x dx$ .

Flashcard 6: What is the integral of $u^n \, du$ ?

Answer: $\frac{u^{n+1}}{n+1} + C$ , $n \neq -1$ . Use the power rule for integration: increase exponent by 1 and divide.

Flashcard 7: What is the integral of $\text{sin } u \, du$ ?

Answer: $-\text{cos } u + C$ . The antiderivative of $\sin u$ is $-\cos u$ plus the constant of integration.

Flashcard 8: What substitution simplifies the integral of $x \text{cos}(x^2)$ ?

Answer: $u = x^2$ . Let $u = x^2$ so that $du = 2x dx$ matches the $x$ factor in $x\cos(x^2)$ .

Flashcard 9: Determine $du$ if $u = x^2 - 1$ in substitution.

Answer: $du = 2x \, dx$ . The derivative of $u = x^2 - 1$ is $2x$ , so $du = 2x dx$ .

Flashcard 10: Find $u$ for substitution if $du = \frac{1}{x^2} \, dx$ .

Answer: $u = -\frac{1}{x}$ . Since $\frac{d}{dx}(-\frac{1}{x}) = \frac{1}{x^2}$ , if $du = \frac{1}{x^2} dx$ , then $u = -\frac{1}{x}$ .

Flashcard 11: Identify $u$ for substitution if $du = 2x \, dx$ .

Answer: $u = x^2$ . Since $\frac{d}{dx}(x^2) = 2x$ , if $du = 2x dx$ , then $u = x^2$ .

Flashcard 12: Find $u$ for substitution if $du = \text{cos } x \, dx$ .

Answer: $u = \text{sin } x$ . Since $\frac{d}{dx}(\sin x) = \cos x$ , if $du = \cos x dx$ , then $u = \sin x$ .

Flashcard 13: What is the integral of $\text{cos } u \, du$ ?

Answer: $\text{sin } u + C$ . The antiderivative of $\cos u$ is $\sin u$ plus the constant of integration.

Flashcard 14: Find $u$ for substitution if $du = 7x^6 \, dx$ .

Answer: $u = x^7$ . Since $\frac{d}{dx}(x^7) = 7x^6$ , if $du = 7x^6 dx$ , then $u = x^7$ .

Flashcard 15: Determine $du$ if $u = \text{ln } x$ in substitution.

Answer: $du = \frac{1}{x} \, dx$ . The derivative of $u = \ln x$ is $\frac{1}{x}$ , so $du = \frac{1}{x} dx$ .

Flashcard 16: Determine $du$ if $u = 3x^4 + 2x$ in substitution.

Answer: $du = (12x^3 + 2) \, dx$ . The derivative of $u = 3x^4 + 2x$ is $12x^3 + 2$ , so $du = (12x^3 + 2) dx$ .

Flashcard 17: What substitution simplifies the integral of $x e^{x^2}$ ?

Answer: $u = x^2$ . Let $u = x^2$ so that $du = 2x dx$ matches the $x$ factor in $xe^{x^2}$ .

Flashcard 18: Identify $u$ for substitution if $du = \text{sec}^2 x \, dx$ .

Answer: $u = \text{tan } x$ . Since $\frac{d}{dx}(\tan x) = \sec^2 x$ , if $du = \sec^2 x dx$ , then $u = \tan x$ .

Flashcard 19: Identify $u$ for substitution if $du = e^x \, dx$ .

Answer: $u = e^x$ . Since $\frac{d}{dx}(e^x) = e^x$ , if $du = e^x dx$ , then $u = e^x$ .

Flashcard 20: Determine $du$ if $u = 2x^3 + 1$ in substitution.

Answer: $du = 6x^2 \, dx$ . The derivative of $u = 2x^3 + 1$ is $6x^2$ , so $du = 6x^2 dx$ .

Flashcard 21: What is the integral of $e^u \, du$ ?

Answer: $e^u + C$ . The antiderivative of $e^u$ is $e^u$ plus the constant of integration.

Flashcard 22: Identify $du$ if $u = x^3$ in substitution.

Answer: $du = 3x^2 \, dx$ . The derivative of $u = x^3$ is $\frac{du}{dx} = 3x^2$ , so $du = 3x^2 dx$ .

Flashcard 23: What substitution simplifies the integral of $\text{cos}(x^2)$ ?

Answer: $u = x^2$ . Let $u = x^2$ to simplify the argument of the cosine function.

Flashcard 24: Find $u$ for substitution if $du = \frac{1}{x} \, dx$ .

Answer: $u = \text{ln } x$ . Since $\frac{d}{dx}(\ln x) = \frac{1}{x}$ , if $du = \frac{1}{x} dx$ , then $u = \ln x$ .

Flashcard 25: What substitution simplifies the integral of $(2x + 1)^5$ ?

Answer: $u = 2x + 1$ . Let $u = 2x + 1$ to transform $(2x + 1)^5$ into $u^5$ for easier integration.

Flashcard 26: What is the substitution for $u$ if $du = -\text{sin } x \, dx$ ?

Answer: $u = \text{cos } x$ . Since $\frac{d}{dx}(\cos x) = -\sin x$ , if $du = -\sin x dx$ , then $u = \cos x$ .

Flashcard 27: Identify $u$ for substitution if $du = 5x^4 \, dx$ .

Answer: $u = x^5$ . Since $\frac{d}{dx}(x^5) = 5x^4$ , if $du = 5x^4 dx$ , then $u = x^5$ .

Flashcard 28: Determine $du$ if $u = \text{ln}(4x)$ in substitution.

Answer: $du = \frac{1}{x} \, dx$ . The derivative of $u = \ln(4x)$ is $\frac{1}{x}$ , so $du = \frac{1}{x} dx$ .

Flashcard 29: What is the integral of $u^n \, du$ ?

Answer: $\frac{u^{n+1}}{n+1} + C$ , $n \neq -1$ . Use the power rule for integration: increase exponent by 1 and divide.

Flashcard 30: Determine $du$ for $u = \text{sin } x$ in substitution.

Answer: $du = \text{cos } x \, dx$ . The derivative of $u = \sin x$ is $\cos x$ , so $du = \cos x dx$ .

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AP Calculus AB Flashcards: Integrating Using Substitution

Study Integrating Using Substitution in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Integrating Using Substitution, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Integrating Using Substitution

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

What substitution simplifies the integral of $(2x + 1)^5$ ?

Tap or drag to reveal answer

ANSWER

$u = 2x + 1$ . Let $u = 2x + 1$ to transform $(2x + 1)^5$ into $u^5$ for easier integration.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: What substitution simplifies the integral of $(2x + 1)^5$ ?

Answer: $u = 2x + 1$ . Let $u = 2x + 1$ to transform $(2x + 1)^5$ into $u^5$ for easier integration.

Flashcard 2: What is the substitution for $u$ if $du = -\text{sin } x \, dx$ ?

Answer: $u = \text{cos } x$ . Since $\frac{d}{dx}(\cos x) = -\sin x$ , if $du = -\sin x dx$ , then $u = \cos x$ .

Flashcard 3: What is the integral of $\frac{1}{u} \, du$ ?

Answer: $\text{ln } |u| + C$ . The antiderivative of $\frac{1}{u}$ is $\ln|u|$ plus the constant of integration.

Flashcard 4: Determine $du$ for $u = \text{sin } x$ in substitution.

Answer: $du = \text{cos } x \, dx$ . The derivative of $u = \sin x$ is $\cos x$ , so $du = \cos x dx$ .

Flashcard 5: Determine $du$ if $u = \text{tan } x$ in substitution.

Answer: $du = \text{sec}^2 x \, dx$ . The derivative of $u = \tan x$ is $\sec^2 x$ , so $du = \sec^2 x dx$ .

Flashcard 6: What is the integral of $u^n \, du$ ?

Answer: $\frac{u^{n+1}}{n+1} + C$ , $n \neq -1$ . Use the power rule for integration: increase exponent by 1 and divide.

Flashcard 7: What is the integral of $\text{sin } u \, du$ ?

Answer: $-\text{cos } u + C$ . The antiderivative of $\sin u$ is $-\cos u$ plus the constant of integration.

Flashcard 8: What substitution simplifies the integral of $x \text{cos}(x^2)$ ?

Answer: $u = x^2$ . Let $u = x^2$ so that $du = 2x dx$ matches the $x$ factor in $x\cos(x^2)$ .

Flashcard 9: Determine $du$ if $u = x^2 - 1$ in substitution.

Answer: $du = 2x \, dx$ . The derivative of $u = x^2 - 1$ is $2x$ , so $du = 2x dx$ .

Flashcard 10: Find $u$ for substitution if $du = \frac{1}{x^2} \, dx$ .

Answer: $u = -\frac{1}{x}$ . Since $\frac{d}{dx}(-\frac{1}{x}) = \frac{1}{x^2}$ , if $du = \frac{1}{x^2} dx$ , then $u = -\frac{1}{x}$ .

Flashcard 11: Identify $u$ for substitution if $du = 2x \, dx$ .

Answer: $u = x^2$ . Since $\frac{d}{dx}(x^2) = 2x$ , if $du = 2x dx$ , then $u = x^2$ .

Flashcard 12: Find $u$ for substitution if $du = \text{cos } x \, dx$ .

Answer: $u = \text{sin } x$ . Since $\frac{d}{dx}(\sin x) = \cos x$ , if $du = \cos x dx$ , then $u = \sin x$ .

Flashcard 13: What is the integral of $\text{cos } u \, du$ ?

Answer: $\text{sin } u + C$ . The antiderivative of $\cos u$ is $\sin u$ plus the constant of integration.

Flashcard 14: Find $u$ for substitution if $du = 7x^6 \, dx$ .

Answer: $u = x^7$ . Since $\frac{d}{dx}(x^7) = 7x^6$ , if $du = 7x^6 dx$ , then $u = x^7$ .

Flashcard 15: Determine $du$ if $u = \text{ln } x$ in substitution.

Answer: $du = \frac{1}{x} \, dx$ . The derivative of $u = \ln x$ is $\frac{1}{x}$ , so $du = \frac{1}{x} dx$ .

Flashcard 16: Determine $du$ if $u = 3x^4 + 2x$ in substitution.

Answer: $du = (12x^3 + 2) \, dx$ . The derivative of $u = 3x^4 + 2x$ is $12x^3 + 2$ , so $du = (12x^3 + 2) dx$ .

Flashcard 17: What substitution simplifies the integral of $x e^{x^2}$ ?

Answer: $u = x^2$ . Let $u = x^2$ so that $du = 2x dx$ matches the $x$ factor in $xe^{x^2}$ .

Flashcard 18: Identify $u$ for substitution if $du = \text{sec}^2 x \, dx$ .

Answer: $u = \text{tan } x$ . Since $\frac{d}{dx}(\tan x) = \sec^2 x$ , if $du = \sec^2 x dx$ , then $u = \tan x$ .

Flashcard 19: Identify $u$ for substitution if $du = e^x \, dx$ .

Answer: $u = e^x$ . Since $\frac{d}{dx}(e^x) = e^x$ , if $du = e^x dx$ , then $u = e^x$ .

Flashcard 20: Determine $du$ if $u = 2x^3 + 1$ in substitution.

Answer: $du = 6x^2 \, dx$ . The derivative of $u = 2x^3 + 1$ is $6x^2$ , so $du = 6x^2 dx$ .

Flashcard 21: What is the integral of $e^u \, du$ ?

Answer: $e^u + C$ . The antiderivative of $e^u$ is $e^u$ plus the constant of integration.

Flashcard 22: Identify $du$ if $u = x^3$ in substitution.

Answer: $du = 3x^2 \, dx$ . The derivative of $u = x^3$ is $\frac{du}{dx} = 3x^2$ , so $du = 3x^2 dx$ .

Flashcard 23: What substitution simplifies the integral of $\text{cos}(x^2)$ ?

Answer: $u = x^2$ . Let $u = x^2$ to simplify the argument of the cosine function.

Flashcard 24: Find $u$ for substitution if $du = \frac{1}{x} \, dx$ .

Answer: $u = \text{ln } x$ . Since $\frac{d}{dx}(\ln x) = \frac{1}{x}$ , if $du = \frac{1}{x} dx$ , then $u = \ln x$ .

Flashcard 25: What substitution simplifies the integral of $(2x + 1)^5$ ?

Answer: $u = 2x + 1$ . Let $u = 2x + 1$ to transform $(2x + 1)^5$ into $u^5$ for easier integration.

Flashcard 26: What is the substitution for $u$ if $du = -\text{sin } x \, dx$ ?

Answer: $u = \text{cos } x$ . Since $\frac{d}{dx}(\cos x) = -\sin x$ , if $du = -\sin x dx$ , then $u = \cos x$ .

Flashcard 27: Identify $u$ for substitution if $du = 5x^4 \, dx$ .

Answer: $u = x^5$ . Since $\frac{d}{dx}(x^5) = 5x^4$ , if $du = 5x^4 dx$ , then $u = x^5$ .

Flashcard 28: Determine $du$ if $u = \text{ln}(4x)$ in substitution.

Answer: $du = \frac{1}{x} \, dx$ . The derivative of $u = \ln(4x)$ is $\frac{1}{x}$ , so $du = \frac{1}{x} dx$ .

Flashcard 29: What is the integral of $u^n \, du$ ?

Answer: $\frac{u^{n+1}}{n+1} + C$ , $n \neq -1$ . Use the power rule for integration: increase exponent by 1 and divide.

Flashcard 30: Determine $du$ for $u = \text{sin } x$ in substitution.

Answer: $du = \text{cos } x \, dx$ . The derivative of $u = \sin x$ is $\cos x$ , so $du = \cos x dx$ .

Opening subject page...

AP Calculus AB Flashcards: Integrating Using Substitution

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Integrating Using Substitution

All flashcards

Flashcard 1: What substitution simplifies the integral of (2x+1)5(2x + 1)^5(2x+1)5?

Flashcard 2: What is the substitution for uuu if du=−sin x dxdu = -\text{sin } x \, dxdu=−sin xdx?

Flashcard 3: What is the integral of 1u du\frac{1}{u} \, duu1​du?

Flashcard 4: Determine dududu for u=sin xu = \text{sin } xu=sin x in substitution.

Flashcard 5: Determine dududu if u=tan xu = \text{tan } xu=tan x in substitution.

Flashcard 6: What is the integral of un duu^n \, duundu?

Flashcard 7: What is the integral of sin u du\text{sin } u \, dusin udu?

Flashcard 8: What substitution simplifies the integral of xcos(x2)x \text{cos}(x^2)xcos(x2)?

Flashcard 9: Determine dududu if u=x2−1u = x^2 - 1u=x2−1 in substitution.

Flashcard 10: Find uuu for substitution if du=1x2 dxdu = \frac{1}{x^2} \, dxdu=x21​dx.

Flashcard 11: Identify uuu for substitution if du=2x dxdu = 2x \, dxdu=2xdx.

Flashcard 12: Find uuu for substitution if du=cos x dxdu = \text{cos } x \, dxdu=cos xdx.

Flashcard 13: What is the integral of cos u du\text{cos } u \, ducos udu?

Flashcard 14: Find uuu for substitution if du=7x6 dxdu = 7x^6 \, dxdu=7x6dx.

Flashcard 15: Determine dududu if u=ln xu = \text{ln } xu=ln x in substitution.

Flashcard 16: Determine dududu if u=3x4+2xu = 3x^4 + 2xu=3x4+2x in substitution.

Flashcard 17: What substitution simplifies the integral of xex2x e^{x^2}xex2?

Flashcard 18: Identify uuu for substitution if du=sec2x dxdu = \text{sec}^2 x \, dxdu=sec2xdx.

Flashcard 19: Identify uuu for substitution if du=ex dxdu = e^x \, dxdu=exdx.

Flashcard 20: Determine dududu if u=2x3+1u = 2x^3 + 1u=2x3+1 in substitution.

Flashcard 21: What is the integral of eu due^u \, dueudu?

Flashcard 22: Identify dududu if u=x3u = x^3u=x3 in substitution.

Flashcard 23: What substitution simplifies the integral of cos(x2)\text{cos}(x^2)cos(x2)?

Flashcard 24: Find uuu for substitution if du=1x dxdu = \frac{1}{x} \, dxdu=x1​dx.

Flashcard 25: What substitution simplifies the integral of (2x+1)5(2x + 1)^5(2x+1)5?

Flashcard 26: What is the substitution for uuu if du=−sin x dxdu = -\text{sin } x \, dxdu=−sin xdx?

Flashcard 27: Identify uuu for substitution if du=5x4 dxdu = 5x^4 \, dxdu=5x4dx.

Flashcard 28: Determine dududu if u=ln(4x)u = \text{ln}(4x)u=ln(4x) in substitution.

Flashcard 29: What is the integral of un duu^n \, duundu?

Flashcard 30: Determine dududu for u=sin xu = \text{sin } xu=sin x in substitution.

Opening subject page...

AP Calculus AB Flashcards: Integrating Using Substitution

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Integrating Using Substitution

All flashcards

Flashcard 1: What substitution simplifies the integral of (2x+1)5(2x + 1)^5(2x+1)5?

Flashcard 2: What is the substitution for uuu if du=−sin x dxdu = -\text{sin } x \, dxdu=−sin xdx?

Flashcard 3: What is the integral of 1u du\frac{1}{u} \, duu1​du?

Flashcard 4: Determine dududu for u=sin xu = \text{sin } xu=sin x in substitution.

Flashcard 5: Determine dududu if u=tan xu = \text{tan } xu=tan x in substitution.

Flashcard 6: What is the integral of un duu^n \, duundu?

Flashcard 7: What is the integral of sin u du\text{sin } u \, dusin udu?

Flashcard 8: What substitution simplifies the integral of xcos(x2)x \text{cos}(x^2)xcos(x2)?

Flashcard 9: Determine dududu if u=x2−1u = x^2 - 1u=x2−1 in substitution.

Flashcard 10: Find uuu for substitution if du=1x2 dxdu = \frac{1}{x^2} \, dxdu=x21​dx.

Flashcard 11: Identify uuu for substitution if du=2x dxdu = 2x \, dxdu=2xdx.

Flashcard 12: Find uuu for substitution if du=cos x dxdu = \text{cos } x \, dxdu=cos xdx.

Flashcard 13: What is the integral of cos u du\text{cos } u \, ducos udu?

Flashcard 14: Find uuu for substitution if du=7x6 dxdu = 7x^6 \, dxdu=7x6dx.

Flashcard 15: Determine dududu if u=ln xu = \text{ln } xu=ln x in substitution.

Flashcard 16: Determine dududu if u=3x4+2xu = 3x^4 + 2xu=3x4+2x in substitution.

Flashcard 17: What substitution simplifies the integral of xex2x e^{x^2}xex2?

Flashcard 18: Identify uuu for substitution if du=sec2x dxdu = \text{sec}^2 x \, dxdu=sec2xdx.

Flashcard 19: Identify uuu for substitution if du=ex dxdu = e^x \, dxdu=exdx.

Flashcard 20: Determine dududu if u=2x3+1u = 2x^3 + 1u=2x3+1 in substitution.

Flashcard 21: What is the integral of eu due^u \, dueudu?

Flashcard 22: Identify dududu if u=x3u = x^3u=x3 in substitution.

Flashcard 23: What substitution simplifies the integral of cos(x2)\text{cos}(x^2)cos(x2)?

Flashcard 24: Find uuu for substitution if du=1x dxdu = \frac{1}{x} \, dxdu=x1​dx.

Flashcard 25: What substitution simplifies the integral of (2x+1)5(2x + 1)^5(2x+1)5?

Flashcard 26: What is the substitution for uuu if du=−sin x dxdu = -\text{sin } x \, dxdu=−sin xdx?

Flashcard 27: Identify uuu for substitution if du=5x4 dxdu = 5x^4 \, dxdu=5x4dx.

Flashcard 28: Determine dududu if u=ln(4x)u = \text{ln}(4x)u=ln(4x) in substitution.

Flashcard 29: What is the integral of un duu^n \, duundu?

Flashcard 30: Determine dududu for u=sin xu = \text{sin } xu=sin x in substitution.

Flashcard 1: What substitution simplifies the integral of $(2x + 1)^5$ ?

Flashcard 2: What is the substitution for $u$ if $du = -\text{sin } x \, dx$ ?

Flashcard 3: What is the integral of $\frac{1}{u} \, du$ ?

Flashcard 4: Determine $du$ for $u = \text{sin } x$ in substitution.

Flashcard 5: Determine $du$ if $u = \text{tan } x$ in substitution.

Flashcard 6: What is the integral of $u^n \, du$ ?

Flashcard 7: What is the integral of $\text{sin } u \, du$ ?

Flashcard 8: What substitution simplifies the integral of $x \text{cos}(x^2)$ ?

Flashcard 9: Determine $du$ if $u = x^2 - 1$ in substitution.

Flashcard 10: Find $u$ for substitution if $du = \frac{1}{x^2} \, dx$ .

Flashcard 11: Identify $u$ for substitution if $du = 2x \, dx$ .

Flashcard 12: Find $u$ for substitution if $du = \text{cos } x \, dx$ .

Flashcard 13: What is the integral of $\text{cos } u \, du$ ?

Flashcard 14: Find $u$ for substitution if $du = 7x^6 \, dx$ .

Flashcard 15: Determine $du$ if $u = \text{ln } x$ in substitution.

Flashcard 16: Determine $du$ if $u = 3x^4 + 2x$ in substitution.

Flashcard 17: What substitution simplifies the integral of $x e^{x^2}$ ?

Flashcard 18: Identify $u$ for substitution if $du = \text{sec}^2 x \, dx$ .

Flashcard 19: Identify $u$ for substitution if $du = e^x \, dx$ .

Flashcard 20: Determine $du$ if $u = 2x^3 + 1$ in substitution.

Flashcard 21: What is the integral of $e^u \, du$ ?

Flashcard 22: Identify $du$ if $u = x^3$ in substitution.

Flashcard 23: What substitution simplifies the integral of $\text{cos}(x^2)$ ?

Flashcard 24: Find $u$ for substitution if $du = \frac{1}{x} \, dx$ .

Flashcard 25: What substitution simplifies the integral of $(2x + 1)^5$ ?

Flashcard 26: What is the substitution for $u$ if $du = -\text{sin } x \, dx$ ?

Flashcard 27: Identify $u$ for substitution if $du = 5x^4 \, dx$ .

Flashcard 28: Determine $du$ if $u = \text{ln}(4x)$ in substitution.

Flashcard 29: What is the integral of $u^n \, du$ ?

Flashcard 30: Determine $du$ for $u = \text{sin } x$ in substitution.

Flashcard 1: What substitution simplifies the integral of $(2x + 1)^5$ ?

Flashcard 2: What is the substitution for $u$ if $du = -\text{sin } x \, dx$ ?

Flashcard 3: What is the integral of $\frac{1}{u} \, du$ ?

Flashcard 4: Determine $du$ for $u = \text{sin } x$ in substitution.

Flashcard 5: Determine $du$ if $u = \text{tan } x$ in substitution.

Flashcard 6: What is the integral of $u^n \, du$ ?

Flashcard 7: What is the integral of $\text{sin } u \, du$ ?

Flashcard 8: What substitution simplifies the integral of $x \text{cos}(x^2)$ ?

Flashcard 9: Determine $du$ if $u = x^2 - 1$ in substitution.

Flashcard 10: Find $u$ for substitution if $du = \frac{1}{x^2} \, dx$ .

Flashcard 11: Identify $u$ for substitution if $du = 2x \, dx$ .

Flashcard 12: Find $u$ for substitution if $du = \text{cos } x \, dx$ .

Flashcard 13: What is the integral of $\text{cos } u \, du$ ?

Flashcard 14: Find $u$ for substitution if $du = 7x^6 \, dx$ .

Flashcard 15: Determine $du$ if $u = \text{ln } x$ in substitution.

Flashcard 16: Determine $du$ if $u = 3x^4 + 2x$ in substitution.

Flashcard 17: What substitution simplifies the integral of $x e^{x^2}$ ?

Flashcard 18: Identify $u$ for substitution if $du = \text{sec}^2 x \, dx$ .

Flashcard 19: Identify $u$ for substitution if $du = e^x \, dx$ .

Flashcard 20: Determine $du$ if $u = 2x^3 + 1$ in substitution.

Flashcard 21: What is the integral of $e^u \, du$ ?

Flashcard 22: Identify $du$ if $u = x^3$ in substitution.

Flashcard 23: What substitution simplifies the integral of $\text{cos}(x^2)$ ?

Flashcard 24: Find $u$ for substitution if $du = \frac{1}{x} \, dx$ .

Flashcard 25: What substitution simplifies the integral of $(2x + 1)^5$ ?

Flashcard 26: What is the substitution for $u$ if $du = -\text{sin } x \, dx$ ?

Flashcard 27: Identify $u$ for substitution if $du = 5x^4 \, dx$ .

Flashcard 28: Determine $du$ if $u = \text{ln}(4x)$ in substitution.

Flashcard 29: What is the integral of $u^n \, du$ ?

Flashcard 30: Determine $du$ for $u = \text{sin } x$ in substitution.