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

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

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integral of ln^2(x)

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

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

Solution steps

\int ln^{2} (x) 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

y^{^{''}} - 4 y^{^{'}} + 4 y = 12 t e^{2 t} + 6 e^{2 t} + 24 - 12 t

\int \frac{1}{( D \cdot E ) - ( D \cdot \frac{F}{G} x )} d x

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

\frac{d}{d x} ((x + 2)^{- 1})

\frac{2 s + 3}{s ^{2} - 4 s + 20}

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