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

The integral of (sin(x))/((3-cos(x))^2) is -1/(3-cos(x))+C

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

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

- \frac{1}{3 - cos ( x )} + C

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Apply u-substitution

= - \int - \frac{1}{v ^{2}} d v

Take the constant out:

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

= - (- \int \frac{1}{v ^{2}} d v)

Apply the Power Rule

= - (- (- \frac{1}{v}))

Substitute back

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

Simplify

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

Add a constant to the solution

= - \frac{1}{3 - cos ( x )} + C

What is the integral of (sin(x))/((3-cos(x))^2) ?
The integral of (sin(x))/((3-cos(x))^2) is -1/(3-cos(x))+C