Tìm nguyên hàm của hàm số sau: ∫x2(x−1)9dx

Question

\(\int x^{2} \left(x-1\right)^{9} {\rm d}x \)

Answer 1

Đặt \(t=x-1\Rightarrow {\rm d}t={\rm d}x\)

\(K=\int \left(t+1\right)^{2} t^{9} {\rm d}t =\int \left(t^{11} +2t^{10} +t^{9} \right) {\rm d}t\)

\(=\frac{1}{12} t^{12} +\frac{2}{11} t^{11} +\frac{1}{10} t^{10} +C.\)

\(=\frac{1}{12} \left(x-1\right)^{12} +\frac{2}{11} \left(x-1\right)^{11} +\frac{1}{10} \left(x-1\right)^{10} +C.\)