Question

Can anyone help me with the process for integration by parts please?

Answer 1

\[\int\limits f(x) g'(x) dx = f(x) g(x) - \int\limits f'(x)g(x) dx\]

Integral must involve a product that can be written f g'.

Choose g' to be a function for which you can find g.

The resulting integral should be simpler than the integral you started with.

Answer 2

Following up from above. You should pick a u that you can easily integrate and a dv that you can easily integrate. This should make the integral easier. A good example of an integral to use by parts on is:
\[\int\limits x \sin(x)dx=-x \cos(x)+\int\limits \cos(x)dx=-x \cos(x)+\sin(x)+C\]
See if you can work that one out.