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

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

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

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

- 4 csc (x) + C

Solution steps

\int 4 \cdot \frac{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

2 x^{2} - 7 x + 5

\frac{\partial}{\partial x} (C e^{2 x})

\frac{x}{x + 1}

\frac{d}{d x} (x^{2} + 5 - 3 x^{- 2})

\int x^{5} cos (y^{4}) d x

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