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

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

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integral of (cot^2(x))/(sin^2(x))

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

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

Solution steps

\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

cos (π t)

\int_{1}^{3} - x^{2} + 4 x - 3 d x

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

\frac{d}{d x} (1 - \frac{x}{2} + \frac{x ^{2}}{9})

\frac{d}{d x} (ln (x e^{x} + 3))

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