What is the integral of (2cos(x))/(3sin^2(x)) ?

The integral of (2cos(x))/(3sin^2(x)) is -2/3 csc(x)+C

integral of (2cos(x))/(3sin^2(x))

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

- \frac{2}{3} csc (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{3} \cdot \int \frac{cos ( x )}{sin ^{2} ( x )} d x

Apply u-substitution

= \frac{2}{3} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= \frac{2}{3} (- \frac{1}{u})

Substitute back

u = sin (x)

= \frac{2}{3} (- \frac{1}{sin ( x )})

Simplify

\frac{2}{3} (- \frac{1}{sin ( x )}) : - \frac{2}{3} csc (x)

= - \frac{2}{3} csc (x)

Add a constant to the solution

= - \frac{2}{3} csc (x) + C

\int_{1}^{2} (4 x^{3} - 3 x^{2} + 2 x) d x

\int cos (3 x - 1) d x

\int (3 t e^{t}, ln (t)) d t

\int \frac{3 x ^{2}}{2} - x - 16.5 d x

2 x^{3} \frac{d y}{d x} = y (2 x^{2} - y^{2})

What is the integral of (2cos(x))/(3sin^2(x)) ?
The integral of (2cos(x))/(3sin^2(x)) is -2/3 csc(x)+C