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

The integral of (cot(x))/(sin^2(x)) is -1/2 csc^2(x)+C

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

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

- \frac{1}{2} csc^{2} (x) + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

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

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

Integral of a constant:

\int a d x = a x

= (- \frac{1}{2}) u

Substitute back

u = csc^{2} (x)

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

Simplify

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

Add a constant to the solution

= - \frac{1}{2} csc^{2} (x) + C

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\frac{\partial}{\partial x} (9 e^{x} ln (y))

\frac{d y}{d x} = (e^{x} + 5)^{2}

What is the integral of (cot(x))/(sin^2(x)) ?
The integral of (cot(x))/(sin^2(x)) is -1/2 csc^2(x)+C