What is the integral of 5sec(x) ?

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

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integral of 5sec(x)

\int 5 sec (x) d x

5 ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int 5 sec (x) d x

Take the constant out:

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

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

Use the common integral:

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

= 5 ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= 5 ln ∣ tan (x) + sec (x) ∣ + C

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