# Integration by substitution

trying to solve the following integral by substitution but having trouble:

$$\int\cos^{5}7x\sin7xdx$$

I attempted to set $$u=\cos^{5}7x$$ and ended up with (by chain rule...which I hope is correct!):

$$du=-35\cos^{4}7x\sin7xdx$$

This doesn't seem too helpful but can't think of a better substitution.

Any advice is appreciated

Andrew

## Answers and Replies

Try using two substitutions. Problems are often made to work out in the end, so try to think of what substitution(s) you can make so things will start to simplify nicely. What if you first set $$u = 7x$$ first? Beautiful things might start to happen. ;)

dextercioby
Well, there's need for only one substitution. $\cos 7 x =u$