What is the integral of csc^3(x)cot(x) ?

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

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integral of csc^3(x)cot(x)

\int csc^{3} (x) cot (x) d x

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

Solution steps

\int csc^{3} (x) cot (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 = csc (x)

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

Add a constant to the solution

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

\int - \frac{x}{x + 1} d x

\int (x + x) d x

\int \frac{ln ( x )}{x ^{3}} d x

\frac{d u}{d u}

d v = cos (3 x) d x

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