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

The integral of ((arctan(x))^4)/(x^2+1) is (arctan^5(x))/5+C

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integral of ((arctan(x))^4)/(x^2+1)

\int \frac{( arctan ( x ) ) ^{4}}{x ^{2} + 1} d x

\frac{arctan ^{5} ( x )}{5} + C

Solution steps

\int \frac{( arctan ( x ) ) ^{4}}{x ^{2} + 1} d x

Apply u-substitution

= \int u^{4} d u

Apply the Power Rule

= \frac{u ^{5}}{5}

Substitute back

u = arctan (x)

= \frac{arctan ^{5} ( x )}{5}

Add a constant to the solution

= \frac{arctan ^{5} ( x )}{5} + C

What is the integral of ((arctan(x))^4)/(x^2+1) ?
The integral of ((arctan(x))^4)/(x^2+1) is (arctan^5(x))/5+C