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

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

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integral of (ln(x))2

\int (ln (x)) 2 d x

2 (x ln (x) - x) + C

Solution steps

\int ln (x) \cdot 2 d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

= 2 (x ln (x) - \int 1 d x)

\int 1 d x = x

= 2 (x ln (x) - x)

Add a constant to the solution

= 2 (x ln (x) - x) + C