What is the integral of (ln(x^3))^2 ?

The integral of (ln(x^3))^2 is 9xln^2(x)-6(3xln(x)-3x)+C

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integral of (ln(x^3))^2

\int (ln (x^{3}))^{2} d x

9 x ln^{2} (x) - 6 (3 x ln (x) - 3 x) + C

Solution steps

\int (ln (x^{3}))^{2} d x

Simplify

= \int ln^{2} (x^{3}) d x

Apply Integration By Parts

: x ln^{2} (x^{3}) - \int 6 ln (x^{3}) d x

= x ln^{2} (x^{3}) - \int 6 ln (x^{3}) d x

\int 6 ln (x^{3}) d x = 6 (3 x ln (x) - 3 x)

= x ln^{2} (x^{3}) - 6 (3 x ln (x) - 3 x)

Simplify

x ln^{2} (x^{3}) - 6 (3 x ln (x) - 3 x) : 9 x ln^{2} (x) - 6 (3 x ln (x) - 3 x)

= 9 x ln^{2} (x) - 6 (3 x ln (x) - 3 x)

Add a constant to the solution

= 9 x ln^{2} (x) - 6 (3 x ln (x) - 3 x) + C

5 y^{^{'}} + 45 y = 9

ln (x^{2} - 2 x)

\int \frac{1}{12 x ^{3}} d x

\int lo g_{2} (x + 2) d x

\int_{0}^{1} e^{x} - 1 d x

What is the integral of (ln(x^3))^2 ?
The integral of (ln(x^3))^2 is 9xln^2(x)-6(3xln(x)-3x)+C