What is the integral of (sin(x))^{1/4}cos(x) ?

The integral of (sin(x))^{1/4}cos(x) is 4/5 sin^{5/4}(x)+C

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integral of (sin(x))^{1/4}cos(x)

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

\frac{4}{5} sin^{\frac{5}{4}} (x) + C

Solution steps

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

Apply u-substitution

: \int u^{\frac{1}{4}} d u

= \int u^{\frac{1}{4}} d u

Apply the Power Rule

: \frac{4}{5} u^{\frac{5}{4}}

= \frac{4}{5} u^{\frac{5}{4}}

Substitute back

u = sin (x)

= \frac{4}{5} sin^{\frac{5}{4}} (x)

Add a constant to the solution

= \frac{4}{5} sin^{\frac{5}{4}} (x) + C

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What is the integral of (sin(x))^{1/4}cos(x) ?
The integral of (sin(x))^{1/4}cos(x) is 4/5 sin^{5/4}(x)+C