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

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

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integral of (sin(x))/((1+cos(x))^3)

\int \frac{sin ( x )}{( 1 + cos ( x ) ) ^{3}} d x

\frac{1}{2 ( 1 + cos ( x ) ) ^{2}} + C

Solution steps

\int \frac{sin ( x )}{( 1 + cos ( x ) ) ^{3}} d x

Apply u-substitution

: \int - \frac{1}{u ^{3}} d u

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

Take the constant out:

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

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

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

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

Substitute back

u = 1 + cos (x)

= - (- \frac{1}{2 ( 1 + cos ( x ) ) ^{2}})

Simplify

= \frac{1}{2 ( 1 + cos ( x ) ) ^{2}}

Add a constant to the solution

= \frac{1}{2 ( 1 + cos ( x ) ) ^{2}} + C

x^{^{''}} = 0

\int cos^{5} (x) sin (x) d x

\frac{d}{d x} (x ln (x + 2))

y^{^{''}} + 16 y = 1 + 2 sin (4 x)

\frac{3 x}{4 - x ^{2}}, at x = 1

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