Question

Họ nguyên hàm của hàm số \(y=\sin ^{2} x\cos ^{3} x\) là:
 

A. \(\sin ^{3} x-\sin ^{5} x+C.\)

B. \(-\frac{1}{3} \sin ^{3} x+\frac{1}{5} \sin ^{5} x+C.\)

C.\( \sin ^{3} x+\sin ^{5} x+C.\)

D.\( \frac{1}{3} \sin ^{3} x-\frac{1}{5} \sin ^{5} x+C. \)

Answer 1

Chọn D
\(F(x)=\int \sin ^{2} x\cos ^{3} xdx =\int \sin ^{2} x(1-\sin ^{2} x)d(\sin x) \)
\(=\int (\sin ^{2} x-\sin ^{4} x) d(\sin x) =\frac{1}{3} \sin ^{3} x-\frac{1}{5} \sin ^{5} x+C.\)