What is the integral of 2sec(4x) ?

The integral of 2sec(4x) is 1/2 ln|tan(4x)+sec(4x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2sec(4x)

\int 2 sec (4 x) d x

\frac{1}{2} ln ∣ tan (4 x) + sec (4 x) ∣ + C

Solution steps

\int 2 sec (4 x) d x

Take the constant out:

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

= 2 \cdot \int sec (4 x) d x

Apply u-substitution

: \int sec (u) \frac{1}{4} d u

= 2 \cdot \int sec (u) \frac{1}{4} d u

Take the constant out:

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

= 2 \cdot \frac{1}{4} \cdot \int sec (u) d u

Use the common integral:

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

= 2 \cdot \frac{1}{4} ln ∣ tan (u) + sec (u) ∣

Substitute back

u = 4 x

= 2 \cdot \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣

Simplify

2 \cdot \frac{1}{4} ln ∣ tan (4 x) + sec (4 x) ∣ : \frac{1}{2} ln ∣ tan (4 x) + sec (4 x) ∣

= \frac{1}{2} ln ∣ tan (4 x) + sec (4 x) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ tan (4 x) + sec (4 x) ∣ + C

\frac{1}{s + 42} - \frac{1}{( s + 3 ) ^{4}}

\int - π cos (1 π) t d t

\frac{\partial}{\partial x} (- 2 e^{3 x})

\frac{d}{d x} (cos (a x))

11 - x^{2}

What is the integral of 2sec(4x) ?
The integral of 2sec(4x) is 1/2 ln|tan(4x)+sec(4x)|+C