What is the integral of (3tan(x))/(cos(x)) ?

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

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integral of (3tan(x))/(cos(x))

\int \frac{3 tan ( x )}{cos ( x )} d x

3 sec (x) + C

Solution steps

\int \frac{3 tan ( x )}{cos ( 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{tan ( x )}{cos ( x )} d x

Rewrite using trig identities

= 3 \cdot \int tan (x) sec (x) d x

Apply u-substitution

= 3 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 3 \cdot 1 \cdot u

Substitute back

u = sec (x)

= 3 \cdot 1 \cdot sec (x)

Simplify

= 3 sec (x)

Add a constant to the solution

= 3 sec (x) + C

What is the integral of (3tan(x))/(cos(x)) ?
The integral of (3tan(x))/(cos(x)) is 3sec(x)+C