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

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

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

integral

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

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

Solution steps

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

Apply u-substitution

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

= \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 + sin (x)

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

Add a constant to the solution

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

\frac{( x ^{4} + 3 )}{x}

- 5 x + 3

\frac{( e ^{- x} ) ^{2}}{y}

(x^{2} - 5 x) e^{x}

\frac{( x + 3 )}{( x ^{2} + 3 )}

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