What is the integral of \sqrt[4]{cos(x)}*sin(x) ?

The integral of \sqrt[4]{cos(x)}*sin(x) is -cos(x)\sqrt[4]{cos(x)}+1/5 cos^{5/4}(x)+C

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integral of \sqrt[4]{cos(x)}*sin(x)

Solution steps

Apply Integration By Parts

\int \frac{1}{4} sin (x) cos^{\frac{1}{4}} (x) d x = - \frac{1}{5} cos^{\frac{5}{4}} (x)

Simplify

Add a constant to the solution

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\int (\frac{3}{8} x - 10)^{5} d x

What is the integral of \sqrt[4]{cos(x)}*sin(x) ?
The integral of \sqrt[4]{cos(x)}*sin(x) is -cos(x)\sqrt[4]{cos(x)}+1/5 cos^{5/4}(x)+C