`intxcot^(2)xdx=?`

Options

A. `-xcotx+(x^(2))/(2)+log|sinx|+C`
B. `-xcotx-(x^(2))/(2)+log|sinx|+C`
C. `-xcotx+(x^(2))/(2)-log|sinx|+C`
D. none of these

Answer

B

Explanation

`I=x("cosec"^(2)x-1)dx=intunderset(I)(x)underset(II)("cosec"^(2))xdx-intxdx`
`=x(-cotx)-int(-cotx)dx-(x^(2))/(2)+C=-xcosx+log|sinx|-(x^(2))/(2)+C`