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

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

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

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

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

Solution steps

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

\frac{1}{( s - 4 )}

\frac{\partial}{\partial y} (x^{2} yz + \frac{1}{x y z ^{2}})

n = 0 \sum \infty (- 1)^{n} x^{n}

\frac{d y}{d x} = 5 y^{2}, y (0) = 3

f (x) = x^{3} - 15 x, (1, - 14)

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