What is the integral of $(x^2)(lnx)$ ?

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Answer 1 · 2018-04-06T00:53:29

$int x^2*Lnx*dx=x^3/3*Lnx-x^3/9+C$

After setting $dv=x^2*dx$ and $u=Lnx$ for using integration by parts, $v=x^3/3$ and $du=dx/x$

Hence,

$int udv=uv-int vdu$

$int x^2*Lnx*dx=x^3/3*Lnx-int x^3/3*dx/x$

= $x^3/3*Lnx-int x^2/3*dx$

= $x^3/3*Lnx-x^3/9+C$

What is the integral of (x^2)(lnx)(x^2)(lnx)?