What is the integral of (cot(x/2))/(sin(x)) ?

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

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integral of (cot(x/2))/(sin(x))

\int \frac{cot ( \frac{x}{2} )}{sin ( x )} d x

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

Solution steps

\int \frac{cot ( \frac{x}{2} )}{sin ( x )} d x

Apply u-substitution

: \int 2 csc (2 u) cot (u) d u

= \int 2 csc (2 u) cot (u) d u

Simplify

2 csc (2 u) cot (u) : csc^{2} (u)

= \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= - cot (u)

Substitute back

u = \frac{x}{2}

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

Add a constant to the solution

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

f (x) = 8 (4 e^{x} - 26)^{4}

x \to 0 lim ((x - 2)^{5})

\frac{1}{s \cdot ( s + 2 )}

x \to 0 lim (\frac{x ^{3}}{x ^{2}})

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

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