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

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

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

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

ln ∣ sec (x) ∣ + C

Solution steps

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

= ln ∣ sec (x) ∣

Add a constant to the solution

= ln ∣ sec (x) ∣ + C

\frac{2 - 5 x}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} (2 x^{3} y + 1)

(3, - 7), (- 10, - 2)

e^{13 x}

\int_{1}^{7} t^{2} - 4 t - 12 d t

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