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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

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

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

Simplify

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

Add a constant to the solution

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

f (x) = 3 x^{2} + 2 x + 1

x^{2} - 4 x + 7, 2 x^{2} - 3 x + 1

y = 4 x^{2} - 5 x

x sin (5 x)

- 2 sin (x), at x = - \frac{π}{3}

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