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

The integral of ln^2(x^2) is 4xln^2(x)-4(2xln(x)-2x)+C

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integral of ln^2(x^2)

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

4 x ln^{2} (x) - 4 (2 x ln (x) - 2 x) + C

Solution steps

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

Apply Integration By Parts

: x ln^{2} (x^{2}) - \int 4 ln (x^{2}) d x

= x ln^{2} (x^{2}) - \int 4 ln (x^{2}) d x

\int 4 ln (x^{2}) d x = 4 (2 x ln (x) - 2 x)

= x ln^{2} (x^{2}) - 4 (2 x ln (x) - 2 x)

Simplify

x ln^{2} (x^{2}) - 4 (2 x ln (x) - 2 x) : 4 x ln^{2} (x) - 4 (2 x ln (x) - 2 x)

= 4 x ln^{2} (x) - 4 (2 x ln (x) - 2 x)

Add a constant to the solution

= 4 x ln^{2} (x) - 4 (2 x ln (x) - 2 x) + C

\int (2 - \frac{1}{x}) ln (x) d x

\frac{d}{d x} (10 sin (x) + 103 cos (x))

y = 9 x - 6 x, (1, 3)

x \to 1 lim (x^{4} - 1)

\int \frac{x ^{5} - x ^{4} + 4 x ^{2} - x}{x ^{3} + 1} d x

What is the integral of ln^2(x^2) ?
The integral of ln^2(x^2) is 4xln^2(x)-4(2xln(x)-2x)+C