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

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

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

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

sec (x) + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (x)

= 1 \cdot sec (x)

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

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