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

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

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integral of (csc^2(x))/(sqrt(3-cot(x)))

\int \frac{csc ^{2} ( x )}{3 - cot ( x )} d x

2 3 - cot (x) + C

Solution steps

\int \frac{csc ^{2} ( x )}{3 - cot ( x )} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 2 u^{\frac{1}{2}}

Substitute back

u = 3 - cot (x)

= 2 (3 - cot (x))^{\frac{1}{2}}

Apply radical rule:

= 2 3 - cot (x)

Add a constant to the solution

= 2 3 - cot (x) + C

\frac{\partial}{\partial x} (- s^{2} t^{2})

t \frac{d y}{d t} + 5 y = t^{3}

\int \frac{1}{8 + 2 x - x ^{2}} d x

x \to \infty lim (8 x^{2})

f (x) = 5 tan (x), at x = 1.57

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