What is the integral of (cot(x))/(sqrt(sin(x))) ?

The integral of (cot(x))/(sqrt(sin(x))) is -2/(sqrt(sin(x)))+C

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integral of (cot(x))/(sqrt(sin(x)))

\int \frac{cot ( x )}{sin ( x )} d x

- \frac{2}{sin ( x )} + C

Solution steps

\int \frac{cot ( x )}{sin ( x )} d x

Apply u-substitution

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

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

Simplify

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

= \int \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

: - \frac{2}{u}

= - \frac{2}{u}

Substitute back

u = sin (x)

= - \frac{2}{sin ( x )}

Add a constant to the solution

= - \frac{2}{sin ( x )} + C

csc (e^{2 x})

\frac{1}{p - p ^{2}} d p = d t

5 x - x^{2}, x, [0, 4]

\frac{d y}{d x} = \frac{e ^{2 x}}{6 y ^{5}}

\int_{1}^{2} 7 r^{2} ln (r) d r

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