What is the integral of (sin^2(x))/(1+cos(x)) ?

The integral of (sin^2(x))/(1+cos(x)) is x-sin(x)+C

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integral of (sin^2(x))/(1+cos(x))

\int \frac{sin ^{2} ( x )}{1 + cos ( x )} d x

x - sin (x) + C

Solution steps

\int \frac{sin ^{2} ( x )}{1 + cos ( x )} d x

Rewrite using trig identities

= \int 1 - cos (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x - \int cos (x) d x

\int 1 d x = x

\int cos (x) d x = sin (x)

= x - sin (x)

Add a constant to the solution

= x - sin (x) + C

y = x + cos (x)

\frac{d}{d x} (\frac{x}{1})

f (x) = \frac{12 x}{1 - x}

\frac{d y}{d x} = y (1 - y^{2})

What is the integral of (sin^2(x))/(1+cos(x)) ?
The integral of (sin^2(x))/(1+cos(x)) is x-sin(x)+C