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

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

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

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

ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

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

Cancel the common factor:

tan (x)

= \int sec (x) d x

Use the common integral:

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= ln ∣ tan (x) + sec (x) ∣ + C

x + 1

f (x) = 2 x - 1

x \to \infty lim (\frac{- 1 ^{x + 1} x}{x + x})

\int \frac{sin ( 2 x )}{39 + cos ^{2} ( x )} d x

f (x) = sin (x^{2} + x)

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