What is the integral of sec(x/2) ?

The integral of sec(x/2) is 2ln|tan(x/2)+sec(x/2)|+C

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integral of sec(x/2)

\int sec (\frac{x}{2}) d x

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

Solution steps

\int sec (\frac{x}{2}) d x

Rewrite using trig identities

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

Apply u-substitution

: \int 2 sec (u) d u

= \int 2 sec (u) d u

Take the constant out:

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

= 2 \cdot \int sec (u) d u

Use the common integral:

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= 2 ln ∣ tan (u) + sec (u) ∣

Substitute back

u = \frac{x}{2}

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

Add a constant to the solution

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

f (x) = 110 x - 16 x^{2}, at 3.438

\frac{x ^{4} - 16 x ^{2} - 16}{( x ^{2} - 4 ) ^{2}}

x y d y - (x^{2} + y^{2}) d x = 0

n = 1 \sum \infty \frac{1}{( 0.8 ) ^{n}}

What is the integral of sec(x/2) ?
The integral of sec(x/2) is 2ln|tan(x/2)+sec(x/2)|+C