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

The integral of x/(1+cos(x)) is xtan(x/2)+2ln|cos(x/2)|+C

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

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

x tan (\frac{x}{2}) + 2 ln cos (\frac{x}{2}) + C

Solution steps

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

Apply Integration By Parts

: x tan (\frac{x}{2}) - \int tan (\frac{x}{2}) d x

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

\int tan (\frac{x}{2}) d x = - 2 ln cos (\frac{x}{2})

= x tan (\frac{x}{2}) - (- 2 ln cos (\frac{x}{2}))

Simplify

= x tan (\frac{x}{2}) + 2 ln cos (\frac{x}{2})

Add a constant to the solution

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

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

f (x) = \frac{x}{x - 3}

f (x) = \frac{x ^{2} + x - 2}{x ^{3} + 6}

\frac{d}{d x} (2 x 4 - x^{2})

\frac{d}{d x} (ln (e^{x} - e^{a}))

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