What is the integral of (sec(x)tan(x))/(sec(x)-8) ?

The integral of (sec(x)tan(x))/(sec(x)-8) is ln|sec(x)-8|+C

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integral of (sec(x)tan(x))/(sec(x)-8)

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 8} d x

ln ∣ sec (x) - 8 ∣ + C

Solution steps

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 8} 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) - 8

= ln ∣ sec (x) - 8 ∣

Add a constant to the solution

= ln ∣ sec (x) - 8 ∣ + C

\frac{d}{d x} (cos (3 x) + sin (3 x))

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{3 t}

\frac{d}{d x} (0.75 - 2 x sin (0.1 x))

y^{^{''}} + 25 y = 10 sin (5 x)

x \to 0 lim (ln (3 - x))

What is the integral of (sec(x)tan(x))/(sec(x)-8) ?
The integral of (sec(x)tan(x))/(sec(x)-8) is ln|sec(x)-8|+C