What is the integral of xln(x)?

Dec 16, 2014

You have to use the Integration by Parts formula: $\int u \mathrm{dv} = u v - \int v \mathrm{du}$

let u= lnx
du = $\frac{1}{x}$

dv = x
v = ${x}^{2} / 2$

Plug this in the IBP formula and you'll get.

=$\ln x \cdot {x}^{2} / 2 - \int {x}^{2} / 2 \cdot \frac{1}{x}$
Solve the integral on the right side and you'll get $- {x}^{2} / 4$

Final answer would be: $\ln x \cdot {x}^{2} / 2 - {x}^{2} / 4$