cleopatra's problems

Question

Evaluate $\int{\frac{9x+6}{(3x-2)^4(x+2)^4}dx}$

Answer 1

$u=(3x-2)(x+2)=3x^2+4x-4$

$u'=6x+4=\frac{2}{3}(9x+6)$

$\displaystyle A=\int{\frac{3}{2}\frac{u'}{u^4}dx}=\frac{3}{2}\int{u^{-4}du}=\frac{3}{2}\cdot\frac{-1}{3}u^{-3}+c=\frac{-1}{2u^3}+c=-\frac{1}{2(3x-2)^3(x+2)^3}+c$