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

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

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

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

ln ∣ arctan (x) ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = arctan (x)

= ln ∣ arctan (x) ∣

Add a constant to the solution

= ln ∣ arctan (x) ∣ + C

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