Question

\(1.\int\dfrac{x^2}{\left(x-1\right)^5}\)dx

Answer 1

Đặt \(x-1=t\Rightarrow dx=dt\)

Ta có:

\(\int\dfrac{x^2}{\left(x-1\right)^5}dx=\int\dfrac{\left(t+1\right)^2}{t^5}dt\)

\(=\int\left(t^{-3}+2t^{-4}+t^{-5}\right)dt\)

\(=\dfrac{t^{-2}}{-2}+2.\dfrac{t^{-3}}{-3}+\dfrac{t^{-4}}{-4}+C\)

\(=\dfrac{-1}{2\left(x-1\right)^2}-\dfrac{2}{3\left(x-1\right)^3}-\dfrac{1}{4\left(x-1\right)^4}+C\)