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

The integral of ((arctan(x))^3)/(1+x^2) is (arctan^4(x))/4+C

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

\int \frac{( arctan ( x ) ) ^{3}}{1 + x ^{2}} d x

\frac{arctan ^{4} ( x )}{4} + C

Solution steps

\int \frac{( arctan ( x ) ) ^{3}}{1 + x ^{2}} d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = arctan (x)

= \frac{arctan ^{4} ( x )}{4}

Add a constant to the solution

= \frac{arctan ^{4} ( x )}{4} + C

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

\int \frac{1}{12 x} d x

\frac{d}{d x} (lo g_{5} (x^{2} - 7 x))

v^{'} = - 0.01 v^{2}

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (1 t)

What is the integral of ((arctan(x))^3)/(1+x^2) ?
The integral of ((arctan(x))^3)/(1+x^2) is (arctan^4(x))/4+C