Question

How do you evaluate `int x/(x^2+2)^3 dx` for [-2, -1]?

Answer 1

`-33/3136`

Explanation:

Use substitution technique and let `u=x^2+3`
Then `du=2xdx`
`therefore 1/2du=xdx`

Limits : `x=-1=>u=4 and x=-2=>u=7`

We may hence re-write this integral as

`1/2int_4^7u^(-3)du=1/2[(u^(-2))/(-2)]_7^4`

`=-1/4(1/16-1/49)=-33/3136`