What is the integral of (sec(x)tan(x))/(1+sec(x)) ?

The integral of (sec(x)tan(x))/(1+sec(x)) is ln|1+sec(x)|+C

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integral of (sec(x)tan(x))/(1+sec(x))

\int \frac{sec ( x ) tan ( x )}{1 + sec ( x )} d x

ln ∣ 1 + sec (x) ∣ + C

Solution steps

\int \frac{sec ( x ) tan ( x )}{1 + sec ( x )} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + sec (x)

= ln ∣ 1 + sec (x) ∣

Add a constant to the solution

= ln ∣ 1 + sec (x) ∣ + C

\frac{d}{d x} (\frac{1}{2 ^{x}})

\int_{0}^{\frac{π}{27}} x tan^{2} (9 x) d x

x \to 0 lim (\frac{tan ( 10 x )}{x})

\frac{d}{d x} (sin (\frac{1}{x - 1}))

y^{^{''}} + 4 y = 3 sin (2 t)

What is the integral of (sec(x)tan(x))/(1+sec(x)) ?
The integral of (sec(x)tan(x))/(1+sec(x)) is ln|1+sec(x)|+C