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

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

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

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

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

Solution steps

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

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

= \int \frac{1}{2} \cdot \frac{1}{1 + cos ( x )} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{1 + cos ( x )} d x

Apply u-substitution

: \int 1 d u

= \frac{1}{2} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2} \cdot 1 \cdot u

Substitute back

u = tan (\frac{x}{2})

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

Simplify

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

Add a constant to the solution

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

\frac{d y}{d x} = x e^{x^{2} - y}

\int x^{3} \cdot e^{x^{2}} d x

\int \frac{8}{x} + 8 x d x

\frac{\partial}{\partial y} (\frac{x}{( x ^{3} + y ^{2} )})

y = - \frac{e ^{- x}}{2} cos (2 x)

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