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

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

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

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

ln ∣ sin (x) + 1 ∣ + C

Solution steps

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

= ln ∣ sin (x) + 1 ∣

Add a constant to the solution

= ln ∣ sin (x) + 1 ∣ + C

\frac{d}{d x} (\frac{sin ( x )}{2})

y = \frac{4 x}{x ^{2} + 1}

f (x) = x^{2.4} + e^{2.4}

\frac{\partial}{\partial x} (5 x^{4} y - 3 y sin (x))

(4.4, 8997.96), (107.3, 21421.44)

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