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

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

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

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

ln ∣ 1 + sin (t) ∣ + C

Solution steps

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

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 (t)

= ln ∣ 1 + sin (t) ∣

Add a constant to the solution

= ln ∣ 1 + sin (t) ∣ + C

\frac{\partial}{\partial x} (x^{2} ln (x))

\int \frac{4 x - 2}{( x ^{2} - x + 1 ) ^{7}} d x

f (x) = ln (cos (2 x))

\int \frac{8}{16 - x ^{2}} d x

y = 7 - x, x = \frac{( y - 4 ) ^{2}}{4}

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