Integration by parts can be used to evaluate complex integrals. For each equation, assign parts to variables following the equation below.

Take the problem below as an example. Assign parts of the integral to be either u or dv. To determine which part should be u, follow the acronym LIPET. Logarithms Inverses Polynomials Exponential Functions Trigonometry

In this equation, there are no logarithms or inverse functions, but there is a polynomial. Because of this, u=, and dv=sinx.

Now, we must solve for du and v. To do this, differentiate u and integrate dv.

Refer back to the equation given on the first slide, and substitute the corresponding parts accordingly.

In this case, we are left with another integral which is too complex, meaning we must integrate by parts again. Following the LIPET acronym, u=2x.

Substitute the parts from the second integration into the result from the first integration.

Finally, integrate the last part of the equation, yielding a final answer.