What is the integral of (log_{e}(x))^2 ?

The integral of (log_{e}(x))^2 is xln^2(x)-2(xln(x)-x)+C

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integral of (log_{e}(x))^2

\int (lo g_{e} (x))^{2} d x

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

Solution steps

\int (lo g_{e} (x))^{2} d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{x ^{2} + 4}{x} d x

\int (\frac{4}{x ^{2}} + 2 - \frac{1}{8 x ^{3}}) d x

\int_{0}^{1} sin (π t) d t

\frac{d}{d x} (\frac{x}{x ^{2} + y ^{2}})

What is the integral of (log_{e}(x))^2 ?
The integral of (log_{e}(x))^2 is xln^2(x)-2(xln(x)-x)+C