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

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

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

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

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

Solution steps

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

Apply u-substitution

= \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}}

Substitute back

u = cot (y)

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

Add a constant to the solution

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

x \to 0 lim (\frac{arcsin ( x )}{7 x})

t \to 0 lim (\frac{e ^{8 t} - 1}{t})

\int e^{x} 2 x d x

\frac{d}{d x} ((\frac{2}{x} + x^{5}) (x^{3} + 1))

\frac{\partial}{\partial p} (arctan (pq r))

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