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

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

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

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

- csc (x) + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

: \int - 1 d u

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = csc (x)

= (- 1) csc (x)

Simplify

= - csc (x)

Add a constant to the solution

= - csc (x) + C

\frac{d}{d x} (sin^{2} (2 x^{3} + 2 x^{2}))

\frac{d}{d x} (x^{2} - 7 x + 10)

\frac{\partial}{\partial x} (ln (5 x + y^{3}))

\frac{d y}{d x} = y (1 - 0.0008 y)

\int \frac{x ^{3} + 4}{x + 2} d x

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