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

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

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

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

- 3 csc (x) + C

Solution steps

\int \frac{3 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

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = sin (x)

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

Simplify

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

= - 3 csc (x)

Add a constant to the solution

= - 3 csc (x) + C

tan (x) + \frac{cos ( x )}{1 + sin ( x )}

\frac{d}{d x} (\frac{x - y}{x})

\int - \frac{1}{2} e^{y} sin (y) d y

\frac{d}{d x} (\frac{686}{( 1 + 7 x ) ^{3}})

y = 2 cos (2 x)

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