`intxcos^(2)xdx=?`

Explanation

`intxcos^(2)xdx=intx((1+cos2x)/(2))dx=(1)/(2)intxdx+(1)/(2)intxcos2xdx`
`=(x^(2))/(4)+(1)/(2)*[x*intcos2xdx-int{(d)/(dx)(x)*intcos2xdx}dx]`
[integrating x cos 2x by parts]
`=(x^(2))/(4)+(1)/(2)[(xsin2x)/(2)-int(sin2x)/(2)dx]`
`=(x^(2))/(4)+(xsin2x)/(4)-(1)/(4)*((-cos2x))/(2)+C`
`=(x^(2))/(4)+(xsin2x)/(4)+(cos2x)/(8)+C`.