Evaluate w.r.t.x , (i) `"in"t x log x dx` (ii) `ing(x^2 - cos x +(1)/(x))dx`

Answer

(i) `(x^2)/(2) (log x- (1)/(2)) + C` (ii) `(x^3)/(3) - sin x + log_e x +C`

Explanation

(i) `int x log xdx = int log x.xdx = log x intxdx -int[(d)/(dx)(logx) int xdx]dx`
`=log x xx(x^2)/(2) - int(1)/(x)xx(x^2)/(2) dx = (x^2)/(2) log x =(x^2)/(4)+C`
`=(x^2)/(2)(log x - (1)/(2))+C`
(ii) `int(x^2 - cos x +(1)/(x)) dx = int x^2 dx -int cos x dx + int (1)/(x) dx= (x^3)/(3) - sin x + log_e x +c`