Question

Integrate the function: x logx

Answer 1

Let I = ∫xlog x dx

Taking log x as first function and x as second function and integrating by parts, we obtain

I = log x∫x dx - ∫{($\frac {d}{dx} log\ x$)∫x dx} dx

I = log x . $\frac {x^2}{2}$ - ∫$\frac 1x$ . $\frac {x^2}{2}$ dx

I = $\frac {x^2log\ x}{2}$ - ∫$\frac x2$ dx

I = $\frac {x^2log\ x}{2}$ - $\frac {x^2}{4}$ + C