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

The integral of (cos(x))/(sin^4(x)) is -1/3 csc^3(x)+C

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integral of (cos(x))/(sin^4(x))

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

- \frac{1}{3} csc^{3} (x) + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{3 u ^{3}}

= - \frac{1}{3 u ^{3}}

Substitute back

u = sin (x)

= - \frac{1}{3 sin ^{3} ( x )}

Simplify

- \frac{1}{3 sin ^{3} ( x )} : - \frac{1}{3} csc^{3} (x)

= - \frac{1}{3} csc^{3} (x)

Add a constant to the solution

= - \frac{1}{3} csc^{3} (x) + C

y^{2} = x^{2} (x + 1)

\frac{6 x}{x ^{2} + 1}

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

- 7 sin (7 x)

n = 1 \sum \infty \frac{n}{( n + 1 )}

What is the integral of (cos(x))/(sin^4(x)) ?
The integral of (cos(x))/(sin^4(x)) is -1/3 csc^3(x)+C