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

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

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

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

- csc (x) + C

Solution steps

\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

\int e^{2 x} - e^{x} d x

\frac{a}{s + a}

\int 4 x^{3} d x

\frac{d}{d x} (\frac{1}{9 x})

\int x a^{x} d x

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