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

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

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

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

- csc (u) + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{v}

= - \frac{1}{v}

Substitute back

v = sin (u)

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

Use the basic trigonometric identity:

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

= - csc (u)

Add a constant to the solution

= - csc (u) + C

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