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

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

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

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

- csc (x) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{cos ( x )}{sin ^{2} ( x )} d x

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = sin (x)

= - \frac{1}{sin ( x )}

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= - csc (x)

Add a constant to the solution

= - csc (x) + C

{(\frac{2}{s} - \frac{1}{s ^{3}})^{2}}

\frac{d}{d x} (8 x^{2} (1 - 3 x)^{5})

\int x^{2} sec (x^{3}) d x

\int (sin (2 x)) e^{s i n^{2} (x)} d x

(sin (3 x))^{^{'}}

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