What is the integral of 3/(sec(x)) ?

The integral of 3/(sec(x)) is 3sin(x)+C

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integral of 3/(sec(x))

\int \frac{3}{sec ( x )} d x

3 sin (x) + C

Solution steps

\int \frac{3}{sec ( x )} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{sec ( x )} d x

Rewrite using trig identities

= 3 \cdot \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= 3 sin (x)

Add a constant to the solution

= 3 sin (x) + C

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