Integration by parts may be useful if you need to integrate over two functions. It is also helpful for integrating the square of a trigonometric function:
example: change sin^2x to (sin x)(sin x) and you have two functions.
The equation for Integration by Parts is shown below:
An example will be shown:
In choosing which will be u and which will be v, it is to our advantage to set u=x because then we have du = 1 dx.
- u = x
- dv = sin x dx
From the above two choices we inherit the following:
- du = 1 dx
- v = – cos x
We then put these four pieces into the equation, omitting the constant of integration until the last line:
As our last step we add the constant of integration:
Rob Sterling 