Finding Indefinite Integrals

Help Questions

Math › Finding Indefinite Integrals

Questions 1 - 10
1

What is the indefinite integral of ?

Explanation

To find the indefinite integral, we use the reverse power rule. That means we raise the exponent on the variables by one and then divide by the new exponent.

Remember to include a when doing integrals. This is a placeholder for any constant that might be in the new expression.

2

Explanation

To find the indefinite integral of , we can use the reverse power rule. To do this, we raise our exponent by one and then divide the variable by that new exponent.

Don't forget to include a to cover any constant!

3

Explanation

To find the indefinite integral, or anti-derivative, we can use the reverse power rule. We raise the exponent of each variable by one and divide by that new exponent.

Don't forget to include a to cover any constant!

Simplify.

4

What is the indefinite integral of ?

Explanation

To solve this problem, we can use the anti-power rule or reverse power rule. We raise the exponent on the variables by one and divide by the new exponent.

For this problem, we'll treat as since anything to the zero power is one.

Since the derivative of any constant is , when we take the indefinite integral, we add a to compensate for any constant that might be there.

From here we can simplify.

5

Explanation

To find the indefinite integral of our given equation, we can use the reverse power rule: we raise the exponent by one and then divide by that new exponent.

Don't forget to include a to compensate for any constant!

6

What is the indefinite integral of ?

Explanation

To find the indefinite integral of our equation, we can use the reverse power rule.

To use the reverse power rule, we raise the exponent of the by one and then divide by that new exponent.

Remember that, when taking the integral, we treat constants as that number times since anything to the zero power is . For example, treat as .

When taking an integral, be sure to include a at the end of everything. stands for "constant". Since taking the derivative of a constant whole number will always equal , we include the to anticipate the possiblity of the equation actually being or instead of just .

7

What is the indefinite integral of ?

Explanation

To solve this problem, we can use the anti-power rule or reverse power rule. We raise the exponent on the variables by one and divide by the new exponent.

For this problem, we'll treat as since anything to the zero power is one.

Since the derivative of any constant is , when we take the indefinite integral, we add a to compensate for any constant that might be there.

From here we can simplify.

8

What is the indefinite integral of ?

Undefined

Explanation

To find the indefinite integral of our equation, we can use the reverse power rule.

To use the reverse power rule, we raise the exponent of the by one and then divide by that new exponent.

Remember that, when taking the integral, we treat constants as that number times , since anything to the zero power is . Treat as .

When taking an integral, be sure to include a . stands for "constant". Since taking the derivative of a constant whole number will always equal , we include the to anticipate the possiblity of the equation actually being or instead of just .

9

Explanation

To integrate , we need to get the two equations in terms of each other. We are going to use "u-substitution" to create a new variable, , which will equal .

Now, if , then

Multiply both sides by to get the more familiar:

Note that our , and our original equation was asking for a positive .

That means if we want in terms of , it looks like this:

Bring the negative sign to the outside:

.

We can use the power rule to find the integral of :

Since we said that , we can plug that back into the equation to get our answer:

10

What is the indefinite integral of ?

Explanation

To solve for the indefinite integral, we can use the reverse power rule. We raise the power of the exponents by one and divide by that new exponent. For this problem, that would look like:

Remember, when taking an integral, definite or indefinite, we always add , as there could be a constant involved.

Page 1 of 3
Return to subject