What is the integral of x\sqrt[4]{81+x^2} ?

The integral of x\sqrt[4]{81+x^2} is 1/2 x^2\sqrt[4]{81+x^2}-1/10 (x^2-324)\sqrt[4]{x^2+81}+C

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integral of x\sqrt[4]{81+x^2}

Solution steps

Apply Integration By Parts

\int \frac{x ^{3}}{4 ( x ^{2} + 81 ) ^{\frac{3}{4}}} d x = \frac{1}{10} (x^{2} - 324) (x^{2} + 81)^{\frac{1}{4}}

Apply radical rule:

Add a constant to the solution

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What is the integral of x\sqrt[4]{81+x^2} ?
The integral of x\sqrt[4]{81+x^2} is 1/2 x^2\sqrt[4]{81+x^2}-1/10 (x^2-324)\sqrt[4]{x^2+81}+C