Question

Integral of `[x/(x^2+4)^3]dx`=?

Answer 1

Let `x^2+4=t`

`dt= 2x dx=> dt/2 = xdx`

`=>intx/(x^2+4)^3dx`

`=>int1/t^3dt/2 =>1/2 int t^-3dt`

`=>1/2 [t^-2/(-2)] +c`

`=>-1/4 [1/t^2] +c`

`=>-1/4 [1/(x^2+4)^2] +c`