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}{u ^{2}} d u

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = 3 + cos (x)

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

Simplify

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

Add a constant to the solution

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

\int_{0}^{b} \frac{1}{4 - x ^{2}} d x

y = 7 cos (x), at x = \frac{π}{3}

y^{^{'}} = 0.4 (10 - x) (5 - x)

\int 5 cos^{2} (x) tan^{3} (x) d x

\frac{d}{d x} (3 arctan (x + 1 + x^{2}))

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