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

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

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integral of (csc(x))^2(cot(x))^2

\int (csc (x))^{2} (cot (x))^{2} d x

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

Solution steps

\int (csc (x))^{2} (cot (x))^{2} 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

\frac{d}{d x} ((3 x^{6} + 4 x^{3})^{4})

\int \frac{x ^{2} - 6 x + 8}{x ^{2} + 2 x + 5} d x

\frac{\partial}{\partial t} (sin^{2} (t))

\int 5 x + 1 d x

\frac{s}{( s ^{2} + 25 ) ^{2}}

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