What is the integral of (sec(u))/(tan(u)) ?

The integral of (sec(u))/(tan(u)) is ln|tan(u/2)|+C

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integral of (sec(u))/(tan(u))

\int \frac{sec ( u )}{tan ( u )} d u

ln tan (\frac{u}{2}) + C

Solution steps

\int \frac{sec ( u )}{tan ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

v = tan (\frac{u}{2})

= ln tan (\frac{u}{2})

Add a constant to the solution

= ln tan (\frac{u}{2}) + C

y = x^{3} - 3 x

\frac{d}{d x} (\frac{1 + sin ( x )}{1 + cos ( x )})

(2 r a^{r x} + n)^{p}

x \to 0 + lim (x^{x^{x}})

\frac{d}{d x} (x - 0.8 - 0.2 sin (x))

What is the integral of (sec(u))/(tan(u)) ?
The integral of (sec(u))/(tan(u)) is ln|tan(u/2)|+C