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

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

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

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

- ln ∣ 1 + cos (x) ∣ + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = 1 + cos (x)

= - ln ∣ 1 + cos (x) ∣

Add a constant to the solution

= - ln ∣ 1 + cos (x) ∣ + C

\frac{1}{x + 8}

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

f (x) = 9 sin (3 x)

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

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

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