What is the integral of 1/(sqrt(sec(x))) ?

The integral of 1/(sqrt(sec(x))) is 2\E(x/2 \vert 2)+C

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integral of 1/(sqrt(sec(x)))

\int \frac{1}{sec ( x )} d x

2 E (\frac{x}{2} ∣2) + C

Solution steps

\int \frac{1}{sec ( x )} d x

Rewrite using trig identities

= \int cos (x) d x

Use the nonelementary integral:

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

= 2 E (\frac{x}{2} ∣ 2)

Add a constant to the solution

= 2 E (\frac{x}{2} ∣ 2) + C

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What is the integral of 1/(sqrt(sec(x))) ?
The integral of 1/(sqrt(sec(x))) is 2\E(x/2 \vert 2)+C