Question

Calcule.
1.$\int\limits {\frac{2x-3}{(x-1)^3} } \, dx$

Answer 1

$\displaystyle\\I=\int\dfrac{2x-3}{(x-1)^3}dx\\\\\text{Seja }u=x-1\text{ ent\~ao temos:}\\\\I=\int\dfrac{2(u+1)-3}{u^3}du=\int\dfrac{2u-1}{u^3}du\\\\\\I=\int\dfrac{2}{u^2}-\dfrac{1}{u^3}du\\\\\\I=2\int\dfrac{1}{u^2}du-\int\dfrac{1}{u^3}du\\\\\\I=-\dfrac{2}{u}+\dfrac{1}{2u^2}+C\\\\\\I=-\dfrac{2}{x-1}+\dfrac{1}{2(x-1)^2}+C$