### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #151 : Calculus

Integrate the following.

**Possible Answers:**

**Correct answer:**

Integration by parts follows the formula:

So, our substitutions will be and

which means and

Plugging our substitutions into the formula gives us:

Since , we have:

, or

### Example Question #1 : Integration By Parts

Evaluate the following integral.

**Possible Answers:**

**Correct answer:**

Integration by parts follows the formula:

In this problem we have so we'll assign our substitutions:

and

which means and

Including our substitutions into the formula gives us:

We can pull out the fraction from the integral in the second part:

Completing the integration gives us:

### Example Question #1 : Integrals

Evaluate the following integral.

**Possible Answers:**

**Correct answer:**

Integration by parts follows the formula:

Our substitutions will be and

which means and .

Plugging our substitutions into the formula gives us:

*Look at the integral: we can pull out the and simplify the remaining as *

.

We now solve the integral: , so:

### Example Question #2 : Integrals

Evaluate the following integral.

**Possible Answers:**

**Correct answer:**

Integration by parts follows the formula:

.

Our substitutions are and

which means and .

Plugging in our substitutions into the formula gives us

*We can pull outside of the integral.*

*Since* , *we have*