What is the integral of (ln(arctan(x)))/(1+x^2) ?

The integral of (ln(arctan(x)))/(1+x^2) is ln(arctan(x))arctan(x)-arctan(x)+C

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integral of (ln(arctan(x)))/(1+x^2)

\int \frac{ln ( arctan ( x ) )}{1 + x ^{2}} d x

ln (arctan (x)) arctan (x) - arctan (x) + C

Solution steps

\int \frac{ln ( arctan ( x ) )}{1 + x ^{2}} d x

Apply Integration By Parts

: ln (arctan (x)) arctan (x) - \int \frac{1}{x ^{2} + 1} d x

= ln (arctan (x)) arctan (x) - \int \frac{1}{x ^{2} + 1} d x

\int \frac{1}{x ^{2} + 1} d x = arctan (x)

= ln (arctan (x)) arctan (x) - arctan (x)

Add a constant to the solution

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

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What is the integral of (ln(arctan(x)))/(1+x^2) ?
The integral of (ln(arctan(x)))/(1+x^2) is ln(arctan(x))arctan(x)-arctan(x)+C