What is the integral of ln^2(x^{20}) ?

The integral of ln^2(x^{20}) is 400xln^2(x)-40(20xln(x)-20x)+C

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integral of ln^2(x^{20})

\int ln^{2} (x^{20}) d x

400 x ln^{2} (x) - 40 (20 x ln (x) - 20 x) + C

Solution steps

\int ln^{2} (x^{20}) d x

Apply Integration By Parts

: x ln^{2} (x^{20}) - \int 40 ln (x^{20}) d x

= x ln^{2} (x^{20}) - \int 40 ln (x^{20}) d x

\int 40 ln (x^{20}) d x = 40 (20 x ln (x) - 20 x)

= x ln^{2} (x^{20}) - 40 (20 x ln (x) - 20 x)

Simplify

x ln^{2} (x^{20}) - 40 (20 x ln (x) - 20 x) : 400 x ln^{2} (x) - 40 (20 x ln (x) - 20 x)

= 400 x ln^{2} (x) - 40 (20 x ln (x) - 20 x)

Add a constant to the solution

= 400 x ln^{2} (x) - 40 (20 x ln (x) - 20 x) + C

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What is the integral of ln^2(x^{20}) ?
The integral of ln^2(x^{20}) is 400xln^2(x)-40(20xln(x)-20x)+C