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

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

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