What is the integral of arctan(\sqrt[3]{x}) ?

The integral of arctan(\sqrt[3]{x}) is xarctan(\sqrt[3]{x})-1/2 (x^{2/3}+1-ln|x^{2/3}+1|)+C

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integral of arctan(\sqrt[3]{x})

Solution steps

Apply Integration By Parts

\int \frac{x ^{\frac{1}{3}}}{3 ( x ^{\frac{2}{3}} + 1 )} d x = \frac{1}{2} (x^{\frac{2}{3}} + 1 - ln x^{\frac{2}{3}} + 1)

Add a constant to the solution

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

\int \frac{x ^{2}}{( x + 5 ) ^{3}} d x

\int \frac{1}{- x + 2} d x

\int \frac{3}{4 - x ^{2}} d x

\int \frac{1}{1 - z ^{2}} d z

What is the integral of arctan(\sqrt[3]{x}) ?
The integral of arctan(\sqrt[3]{x}) is xarctan(\sqrt[3]{x})-1/2 (x^{2/3}+1-ln|x^{2/3}+1|)+C