What is the integral of (cos(x))/((1+sin(x))^5) ?

The integral of (cos(x))/((1+sin(x))^5) is -1/(4(1+sin(x))^4)+C

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integral of (cos(x))/((1+sin(x))^5)

\int \frac{cos ( x )}{( 1 + sin ( x ) ) ^{5}} d x

- \frac{1}{4 ( 1 + sin ( x ) ) ^{4}} + C

Solution steps

\int \frac{cos ( x )}{( 1 + sin ( x ) ) ^{5}} d x

Apply u-substitution

: \int \frac{1}{u ^{5}} d u

= \int \frac{1}{u ^{5}} d u

Apply the Power Rule

: - \frac{1}{4 u ^{4}}

= - \frac{1}{4 u ^{4}}

Substitute back

u = 1 + sin (x)

= - \frac{1}{4 ( 1 + sin ( x ) ) ^{4}}

Add a constant to the solution

= - \frac{1}{4 ( 1 + sin ( x ) ) ^{4}} + C

\frac{d}{d x} ((e^{x^{2}} + 4)^{2} \cdot (4 x)^{3 x})

\frac{16}{s ( s ^{2} + 16 )}

x \to 0 lim (\frac{2}{sin ( 3 x )})

n = 1 \sum \infty \frac{7}{2 ^{n}}

\frac{d}{d x} (\frac{9 x ^{2}}{x ^{2} + 2})

What is the integral of (cos(x))/((1+sin(x))^5) ?
The integral of (cos(x))/((1+sin(x))^5) is -1/(4(1+sin(x))^4)+C