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

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

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

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

- \frac{2}{3} cot^{\frac{3}{2}} (x) + C

Solution steps

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

Apply u-substitution

: \int - u d u

= \int - u d u

Take the constant out:

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

= - \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= - \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = cot (x)

= - \frac{2}{3} cot^{\frac{3}{2}} (x)

Add a constant to the solution

= - \frac{2}{3} cot^{\frac{3}{2}} (x) + C

\frac{1}{x - 1}, x = 20

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

x \to 0 lim (- e^{- x})

\frac{\partial}{\partial x} (2 x + 1 - 5 y)

h (x) = 3 + 5 sin (x)

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