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

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

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

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

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

Solution steps

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

\frac{d}{d x} (x ln (6 x))

\frac{\partial}{\partial x} (sin (\frac{x \cdot y}{y - 4}))

\int 1 + \frac{x}{x ^{2} + y ^{2}} d y

f (x) = 8 x^{2} - x^{3}, at x = 2

\frac{\partial}{\partial x} (\frac{y}{2 x})

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