What is the integral of sec(2t) ?

The integral of sec(2t) is 1/2 ln|tan(2t)+sec(2t)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sec(2t)

\int sec (2 t) d t

\frac{1}{2} ln ∣ tan (2 t) + sec (2 t) ∣ + C

Solution steps

\int sec (2 t) d t

Apply u-substitution

= \int sec (u) \frac{1}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int sec (u) d u

Use the common integral:

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

= \frac{1}{2} ln ∣ tan (u) + sec (u) ∣

Substitute back

u = 2 t

= \frac{1}{2} ln ∣ tan (2 t) + sec (2 t) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ tan (2 t) + sec (2 t) ∣ + C

What is the integral of sec(2t) ?
The integral of sec(2t) is 1/2 ln|tan(2t)+sec(2t)|+C