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

: x ln (x) - \int 1 d x

= 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

\frac{ln ( x )}{ln ( 2 )}

\int \frac{4 x ^{2} + 9}{x ^{4}} d x

\int \frac{x}{9 + x ^{4}} d x

\frac{1 + 0.5 x}{1 - 0.5 x}

\frac{d}{d x} (\frac{3 x}{2 x ^{2} + 1})