GRE Subject Test: Math : Integration by Parts

Example Questions

Example Question #5 : Integrals

Integrate the following.      Explanation:

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 #6 : Integrals

Evaluate the following integral.      Explanation:

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.      Explanation:

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 #1 : Integration By Parts

Evaluate the following integral.      Explanation:

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  All GRE Subject Test: Math Resources 