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

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

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

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

- \frac{1}{4 ( 5 + sin ( x ) ) ^{4}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{( 5 + u ) ^{5}} d u

= \int \frac{1}{( 5 + u ) ^{5}} d u

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

= - \frac{1}{4 ( 5 + sin ( x ) ) ^{4}}

Add a constant to the solution

= - \frac{1}{4 ( 5 + sin ( x ) ) ^{4}} + C

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