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 u d u

(ln^{3} (x))^{^{'}}

\int (sin (x))^{5} (cos (x))^{3} d x

\frac{d ^{2}}{d x ^{2}} (1 + \frac{1}{x ^{4}})

\frac{3}{x}

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