What is the antiderivative of $x ln x$ ?

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Answer 1 · 2016-04-19T22:13:52

$intxlnxdx=(x^2lnx)/2-x^2/4+C$

$intudv=uv-intvdu$

In the case of

$intxlnxdx$

We let

$u=lnx" "=>" "(du)/dx=1/x" "=>" "du=1/xdx$

$dv=xdx" "=>" "intdv=intxdx" "=>" "v=x^2/2$

Thus, plugging these in, we see that

$intxlnxdx=(x^2/2)lnx-intx^2/2(1/x)dx$

$=(x^2lnx)/2-intx/2dx$

$=(x^2lnx)/2-x^2/4+C$

What is the antiderivative of x ln x x ln x ?