What is the integral of sec(t)sec(t)+tan(t) ?

The integral of sec(t)sec(t)+tan(t) is tan(t)-ln|cos(t)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sec(t)sec(t)+tan(t)

\int sec (t) sec (t) + tan (t) d t

tan (t) - ln ∣ cos (t) ∣ + C

Solution steps

\int sec (t) sec (t) + tan (t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sec (t) sec (t) d t + \int tan (t) d t

\int sec (t) sec (t) d t = tan (t)

\int tan (t) d t = - ln ∣ cos (t) ∣

= tan (t) - ln ∣ cos (t) ∣

Add a constant to the solution

= tan (t) - ln ∣ cos (t) ∣ + C

What is the integral of sec(t)sec(t)+tan(t) ?
The integral of sec(t)sec(t)+tan(t) is tan(t)-ln|cos(t)|+C