What is the integral of sec(x/7) ?

The integral of sec(x/7) is 7ln|tan(x/7)+sec(x/7)|+C

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integral of sec(x/7)

\int sec (\frac{x}{7}) d x

7 ln tan (\frac{x}{7}) + sec (\frac{x}{7}) + C

Solution steps

\int sec (\frac{x}{7}) d x

Apply u-substitution

: \int sec (u) \cdot 7 d u

= \int sec (u) \cdot 7 d u

Take the constant out:

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

= 7 \cdot \int sec (u) d u

Use the common integral:

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

= 7 ln ∣ tan (u) + sec (u) ∣

Substitute back

u = \frac{x}{7}

= 7 ln tan (\frac{x}{7}) + sec (\frac{x}{7})

Add a constant to the solution

= 7 ln tan (\frac{x}{7}) + sec (\frac{x}{7}) + C

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What is the integral of sec(x/7) ?
The integral of sec(x/7) is 7ln|tan(x/7)+sec(x/7)|+C