What is the integral of (cos(x))/(sin^5(x)) ?

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

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integral of (cos(x))/(sin^5(x))

\int \frac{cos ( x )}{sin ^{5} ( x )} d x

- \frac{1}{4} csc^{4} (x) + C

Solution steps

\int \frac{cos ( x )}{sin ^{5} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{5}} d u

= \int \frac{1}{u ^{5}} d u

Apply the Power Rule

: - \frac{1}{4 u ^{4}}

= - \frac{1}{4 u ^{4}}

Substitute back

u = sin (x)

= - \frac{1}{4 sin ^{4} ( x )}

Simplify

- \frac{1}{4 sin ^{4} ( x )} : - \frac{1}{4} csc^{4} (x)

= - \frac{1}{4} csc^{4} (x)

Add a constant to the solution

= - \frac{1}{4} csc^{4} (x) + C

f (x) = \frac{x ^{3} - 3 x ^{2} + 4}{x ^{2}}

\frac{d}{d x} (e^{x} \cdot cos (x))

\frac{\partial}{\partial x} (6 x e^{x + y})

x \to 3 - lim (2 3 - x)

\frac{d}{d y} (- y^{2})

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