What is the integral of (sec(x)tan(x))/(sec(x)-2) ?

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

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integral of (sec(x)tan(x))/(sec(x)-2)

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 2} d x

ln ∣ sec (x) - 2 ∣ + C

Solution steps

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 2} 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 = sec (x) - 2

= ln ∣ sec (x) - 2 ∣

Add a constant to the solution

= ln ∣ sec (x) - 2 ∣ + C

\frac{d y}{d t} - 5 y = - 9 e^{2 t}

\frac{2 x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x + 6

x \to 2 lim (ln (x))

\int \frac{1}{x ^{2} 16 - x} d x

- \frac{5}{x ^{3}}, at x = 9

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