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

\frac{d}{d x} (x^{2} + 36)

\int \frac{- 3 x + 2}{x ^{3} + x ^{2} - 2} d x

\int (\frac{3}{u ^{2}} + \frac{4}{u ^{3}} - 2) d u

y^{^{''}} - 4 y^{^{'}} = sin (3 x)

7 x^{6} - 4 x^{5}

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