What is the integral of (x^2)(lnx)(x2)(lnx)?

1 Answer
Cem Sentin
Apr 6, 2018

int x^2*Lnx*dx=x^3/3*Lnx-x^3/9+C∫x2⋅lnx⋅dx=x33⋅lnx−x39+C

Explanation:

After setting dv=x^2*dxdv=x2⋅dx and u=Lnxu=lnx for using integration by parts, v=x^3/3v=x33 and du=dx/xdu=dxx

Hence,

int udv=uv-int vdu∫udv=uv−∫vdu

int x^2*Lnx*dx=x^3/3*Lnx-int x^3/3*dx/x∫x2⋅lnx⋅dx=x33⋅lnx−∫x33⋅dxx

=x^3/3*Lnx-int x^2/3*dxx33⋅lnx−∫x23⋅dx

=x^3/3*Lnx-x^3/9+Cx33⋅lnx−x39+C

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