What is the integral of x*\sqrt[4]{x^{11}} ?

The integral of x*\sqrt[4]{x^{11}} is 4/19 x^{19/4}+C

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integral of x*\sqrt[4]{x^{11}}

\frac{4}{19} x^{\frac{19}{4}} + C

Solution steps

assuming

x \geq 0

= \int x x^{\frac{11}{4}} d x

Simplify

x x^{\frac{11}{4}} : x^{\frac{15}{4}}

= \int x^{\frac{15}{4}} d x

Apply the Power Rule

: \frac{4}{19} x^{\frac{19}{4}}

= \frac{4}{19} x^{\frac{19}{4}}

Add a constant to the solution

= \frac{4}{19} x^{\frac{19}{4}} + C

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What is the integral of x*\sqrt[4]{x^{11}} ?
The integral of x*\sqrt[4]{x^{11}} is 4/19 x^{19/4}+C