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

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

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

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

ln ∣ 1 + sin (z) ∣ + C

Solution steps

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

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 (z)

= ln ∣ 1 + sin (z) ∣

Add a constant to the solution

= ln ∣ 1 + sin (z) ∣ + C

\int 0.2 x + 1 d x

sec^{2} (\frac{x}{2})

\int x (2 - x^{2})^{3} d x

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

\int sec^{2} (x) tan^{1} (x) d x

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