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

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

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

\int cot (x) csc (x) d x

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

Solution steps

\int cot (x) csc (x) d x

Rewrite using trig identities

= \int \frac{cos ( x )}{sin ( x ) sin ( x )} d x

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= \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

\frac{d}{d x} (x - 8)

\int 2 + x d x

y = - x^{3}, (- 1, 1)

y = \frac{x + 3}{x ^{3} + x - 1}

\frac{\partial}{\partial x} (14 - x^{2} - 4 x y)

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