What is the integral of (cos^2(x))/(sin^4(x)) ?

The integral of (cos^2(x))/(sin^4(x)) is -(cot^3(x))/3+C

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integral of (cos^2(x))/(sin^4(x))

\int \frac{cos ^{2} ( x )}{sin ^{4} ( x )} d x

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

Solution steps

\int \frac{cos ^{2} ( x )}{sin ^{4} ( x )} d x

Rewrite using trig identities

= \int \frac{cot ^{2} ( x )}{sin ^{2} ( x )} d x

Apply u-substitution

: \int - u^{2} d u

= \int - u^{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = cot (x)

= - \frac{cot ^{3} ( x )}{3}

Add a constant to the solution

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

n = 3 \sum \infty \frac{5}{9 ^{n}}

\frac{\partial}{\partial y} (x - y^{3} + y^{2} sin (x))

e^{(\frac{2}{x})}

\int_{- 2}^{2} - 3 x^{2} - 4 x d x

\int \frac{5}{x ^{2} + 3 x - 4} d x

What is the integral of (cos^2(x))/(sin^4(x)) ?
The integral of (cos^2(x))/(sin^4(x)) is -(cot^3(x))/3+C