What is the integral of (4cos(x))/(sin^2(x)) ?

The integral of (4cos(x))/(sin^2(x)) is -4csc(x)+C

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integral of (4cos(x))/(sin^2(x))

\int \frac{4 cos ( x )}{sin ^{2} ( x )} d x

- 4 csc (x) + C

Solution steps

\int \frac{4 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

= 4 \cdot \int \frac{cos ( x )}{sin ^{2} ( x )} d x

Apply u-substitution

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

= 4 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 4 (- \frac{1}{u})

Substitute back

u = sin (x)

= 4 (- \frac{1}{sin ( x )})

Simplify

4 (- \frac{1}{sin ( x )}) : - 4 csc (x)

= - 4 csc (x)

Add a constant to the solution

= - 4 csc (x) + C

y = cos (x), at x = 1

\frac{d}{d x} (\frac{x ^{3} + 8}{x ^{2} - 4})

\int \frac{1}{2} d x

\int_{1}^{2} \frac{1}{x - 1} d x

\int \frac{16}{x ^{2} - 1} d x

What is the integral of (4cos(x))/(sin^2(x)) ?
The integral of (4cos(x))/(sin^2(x)) is -4csc(x)+C