What is the integral of $xln(x)$ ?

Question

1950 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-12-16T09:07:54

You have to use the Integration by Parts formula: $intudv=uv-intvdu$

let u= lnx
du = $1/x$

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

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

= $lnx*x^2/2 - intx^2/2*1/x$
Solve the integral on the right side and you'll get $-x^2/4$

Final answer would be: $lnx*x^2/2-x^2/4$

What is the integral of xln(x)xln(x)?