`intxsin^(3)x^(2)cosx^(2)dx=?`

Options

A. `(1)/(4)sin^(4)x^(2)+C`
B. `(1)/(8)sin^(4)x^(2)+C`
C. `(1)/(2)sin^(4)x^(2)+C`
D. none of these

Answer

B

Explanation

Put `sinx^(2)=t and2xcosx^(2)dx=dt`.
`:." "I=(1)/(2)intt^(3)dt=(1)/(2)xx(t^(4))/(4)+C=(t^(4))/(8)+C=(1)/(8)sin^(4)x^(2)+C`.