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

The integral of (sin(x))/(1+sin(x)) is 2/(tan(x/2)+1)+x+C

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

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

\frac{2}{tan ( \frac{x}{2} ) + 1} + x + C

Solution steps

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

\frac{sin ( x )}{1 + sin ( x )} = - \frac{1}{1 + sin ( x )} + 1

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

\int \frac{1}{1 + sin ( x )} d x = - \frac{2}{tan ( \frac{x}{2} ) + 1}

\int 1 d x = x

= - (- \frac{2}{tan ( \frac{x}{2} ) + 1}) + x

Simplify

= \frac{2}{tan ( \frac{x}{2} ) + 1} + x

Add a constant to the solution

= \frac{2}{tan ( \frac{x}{2} ) + 1} + x + C

y^{^{'}} + (x + 2) y^{2} = 0

x \to \infty lim (\frac{2 x ^{2}}{x + 3})

\frac{\partial}{\partial x} (e^{a x} cos (b x + y))

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

y = 49 - x^{2}, (- 7, 0)

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