What is the integral of (cos(x))/(sin^6(x)) ?

The integral of (cos(x))/(sin^6(x)) is -1/5 csc^5(x)+C

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integral of (cos(x))/(sin^6(x))

\int \frac{cos ( x )}{sin ^{6} ( x )} d x

- \frac{1}{5} csc^{5} (x) + C

Solution steps

\int \frac{cos ( x )}{sin ^{6} ( x )} d x

Apply u-substitution

= \int \frac{1}{u ^{6}} d u

Apply the Power Rule

= - \frac{1}{5 u ^{5}}

Substitute back

u = sin (x)

= - \frac{1}{5 sin ^{5} ( x )}

Simplify

- \frac{1}{5 sin ^{5} ( x )} : - \frac{1}{5} csc^{5} (x)

= - \frac{1}{5} csc^{5} (x)

Add a constant to the solution

= - \frac{1}{5} csc^{5} (x) + C

What is the integral of (cos(x))/(sin^6(x)) ?
The integral of (cos(x))/(sin^6(x)) is -1/5 csc^5(x)+C