What is the integral of (sec(x))/2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sec(x))/2

\int \frac{sec ( x )}{2} d x

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

Solution steps

\int \frac{sec ( x )}{2} d x

Take the constant out:

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

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

Use the common integral:

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

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

Add a constant to the solution

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

x \to + \frac{7}{8} lim (x^{4})

\frac{d}{d x} (sinh (cosh (x^{3})))

\frac{d}{d x} (1 + 2 tan (x))

\frac{d}{d x} (\frac{8 x}{e ^{x}})

y = e^{2 x}, y = e^{- 2 x}, x = 1

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