What is the integral of sec(x/5) ?

The integral of sec(x/5) is 5ln|tan(x/5)+sec(x/5)|+C

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integral of sec(x/5)

\int sec (\frac{x}{5}) d x

5 ln tan (\frac{x}{5}) + sec (\frac{x}{5}) + C

Solution steps

\int sec (\frac{x}{5}) d x

Apply u-substitution

: \int sec (u) \cdot 5 d u

= \int sec (u) \cdot 5 d u

Take the constant out:

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

= 5 \cdot \int sec (u) d u

Use the common integral:

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

= 5 ln ∣ tan (u) + sec (u) ∣

Substitute back

u = \frac{x}{5}

= 5 ln tan (\frac{x}{5}) + sec (\frac{x}{5})

Add a constant to the solution

= 5 ln tan (\frac{x}{5}) + sec (\frac{x}{5}) + C

\frac{1}{s ( s ^{2} + 5 s + 6 )}

x \to 0 lim (x sin (\frac{1}{x ^{2}}))

f (x) = \frac{x}{x - 1}

f (x) = 6^{x}

\int \frac{1}{x ^{2} 25 + x ^{2}} d x

What is the integral of sec(x/5) ?
The integral of sec(x/5) is 5ln|tan(x/5)+sec(x/5)|+C