# Calculus 1 : How to find integral expressions

## Example Questions

### Example Question #91 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

### Example Question #92 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Explanation:

To solve this problem we have to use a u substitution. We also need to remember our properties of trig functions. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

### Example Question #93 : Equations

Evaluate the following indefinite integral:

Explanation:

To solve this problem, all we have to remember is that the integral of e doesn't change. That gives us the following:

### Example Question #93 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

### Example Question #94 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

### Example Question #95 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Explanation:

To solve this integral, we use the power rule for the first term:

And use the laws of trig functions for the second term:

We can combine these terms and add our "C" to get the final answer:

### Example Question #96 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

### Example Question #97 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

### Example Question #98 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

### Example Question #99 : How To Find Integral Expressions

Evaluate the following indefinite integral: