What is the integral of ln^2(ax) ?

The integral of ln^2(ax) is xln^2(ax)-2(xln(ax)-x)+C

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integral of ln^2(ax)

\int ln^{2} (a x) d x

x ln^{2} (a x) - 2 (x ln (a x) - x) + C

Solution steps

\int ln^{2} (a x) d x

Apply Integration By Parts

: x ln^{2} (a x) - \int 2 ln (a x) d x

= x ln^{2} (a x) - \int 2 ln (a x) d x

\int 2 ln (a x) d x = 2 (x ln (a x) - x)

= x ln^{2} (a x) - 2 (x ln (a x) - x)

Add a constant to the solution

= x ln^{2} (a x) - 2 (x ln (a x) - x) + C

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What is the integral of ln^2(ax) ?
The integral of ln^2(ax) is xln^2(ax)-2(xln(ax)-x)+C