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

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

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

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

- \frac{1}{arctan ( x )} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = arctan (x)

= - \frac{1}{arctan ( x )}

Add a constant to the solution

= - \frac{1}{arctan ( x )} + C

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