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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \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

x \to 0 lim (ln ((\frac{1}{x})^{x}))

\int (\frac{ln ( x )}{x ^{3}}) d x

\frac{d}{d x} (\frac{10}{( x - 2 ) ^{3}})

\frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})

\frac{\partial}{\partial x} (6 x + 2 y)

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