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

The integral of (cos(x))/((1+sin(x))) is ln|1+sin(x)|+C

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

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

ln ∣ 1 + sin (x) ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + sin (x)

= ln ∣ 1 + sin (x) ∣

Add a constant to the solution

= ln ∣ 1 + sin (x) ∣ + C

f (x) = 2 x^{3} - 3 x^{2} - 36 x + 5

f (x) = cos (a x)

x \to \infty + lim (ln (x))

\int π sin (π x) d x

\int \frac{1}{2 - 5 x} d x

What is the integral of (cos(x))/((1+sin(x))) ?
The integral of (cos(x))/((1+sin(x))) is ln|1+sin(x)|+C