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

The integral of (sec(3x))/(cot(3x)) is 1/3 sec(3x)+C

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integral of (sec(3x))/(cot(3x))

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

\frac{1}{3} sec (3 x) + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

= \int \frac{1}{3} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3} u

Substitute back

u = sec (3 x)

= \frac{1}{3} sec (3 x)

Add a constant to the solution

= \frac{1}{3} sec (3 x) + C

What is the integral of (sec(3x))/(cot(3x)) ?
The integral of (sec(3x))/(cot(3x)) is 1/3 sec(3x)+C