Question

Evaluate the following?

`int(x^7)/(1+x^4)^2`

Answer 1

`1/4*(ln(1+x^4)+1/(1+x^4))+C`

Explanation:

`intx^7/(1+x^4)^2dx`
Let `u=1+x^4` then `(du)/dx=4x^3`
`intx^7/(u)^2*1/(4x^3)(du)/dxdx`
`1/4intx^4/(u)^2du`
Use `u=1+x^4<=>x^4=u-1`
`1/4int(u-1)/(u)^2du`
`1/4int1/u-1/u^2du`
`1/4*(ln(u)+1/u)+C`
Insert `u=1+x^4`
`1/4*(ln(1+x^4)+1/(1+x^4))+C`