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

The integral of ((arctan(x))^2)/(1+x^2) is (arctan^3(x))/3+C

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

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

\frac{arctan ^{3} ( x )}{3} + C

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = arctan (x)

= \frac{arctan ^{3} ( x )}{3}

Add a constant to the solution

= \frac{arctan ^{3} ( x )}{3} + C

y y^{^{'}} + x y^{2} = (e^{- x^{2}})

f (x) = \frac{1}{3} x^{3} + 5.5 x^{2} + 30 x + 22

x \to 0 + lim (\frac{x ^{x} - 1}{2 x})

t \to 0 lim (1 + t^{3})

\int \frac{1}{12} cot (3 x) d x

What is the integral of ((arctan(x))^2)/(1+x^2) ?
The integral of ((arctan(x))^2)/(1+x^2) is (arctan^3(x))/3+C