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

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

Popular >

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

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

2 csc (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = sin (x)

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

Simplify

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

= 2 csc (x)

Add a constant to the solution

= 2 csc (x) + C

\frac{d}{d x} (x e^{\frac{1}{2}})

\int_{0}^{π} 10 sin^{4} (x) d x

\int \frac{17}{x ^{2} + 1} d x

y^{^{''}} - 8 y^{^{'}} + 32 y = 0

5 x (x - 1)

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