What is the integral of (cos(x))/(sin^{7/4)(x)} ?

The integral of (cos(x))/(sin^{7/4)(x)} is -4/(3sin^{3/4)(x)}+C

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integral of (cos(x))/(sin^{7/4)(x)}

\int \frac{cos ( x )}{sin ^{\frac{7}{4}} ( x )} d x

- \frac{4}{3 sin ^{\frac{3}{4}} ( x )} + C

Solution steps

\int \frac{cos ( x )}{sin ^{\frac{7}{4}} ( x )} d x

Apply u-substitution

= \int \frac{1}{u ^{\frac{7}{4}}} d u

Apply the Power Rule

= - \frac{4}{3 u ^{\frac{3}{4}}}

Substitute back

u = sin (x)

= - \frac{4}{3 sin ^{\frac{3}{4}} ( x )}

Add a constant to the solution

= - \frac{4}{3 sin ^{\frac{3}{4}} ( x )} + C

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What is the integral of (cos(x))/(sin^{7/4)(x)} ?
The integral of (cos(x))/(sin^{7/4)(x)} is -4/(3sin^{3/4)(x)}+C