What is the integral of 1/(cos(8x)) ?

The integral of 1/(cos(8x)) is 1/8 ln|tan(8x)+sec(8x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(cos(8x))

\int \frac{1}{cos ( 8 x )} d x

\frac{1}{8} ln ∣ tan (8 x) + sec (8 x) ∣ + C

Solution steps

\int \frac{1}{cos ( 8 x )} d x

Rewrite using trig identities

= \int sec (8 x) d x

Apply u-substitution

: \int sec (u) \frac{1}{8} d u

= \int sec (u) \frac{1}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int sec (u) d u

Use the common integral:

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

= \frac{1}{8} ln ∣ tan (u) + sec (u) ∣

Substitute back

u = 8 x

= \frac{1}{8} ln ∣ tan (8 x) + sec (8 x) ∣

Add a constant to the solution

= \frac{1}{8} ln ∣ tan (8 x) + sec (8 x) ∣ + C

\int_{0}^{2} 6 x (2 - x) d x

(2 x - 3) e^{2 - x}

\frac{d}{d x} (x^{2} + 2 y^{2})

\frac{d}{d x} (x^{3} - 3 x^{2} + 2)

y = x^{2} - 2, (- 3, 7)

What is the integral of 1/(cos(8x)) ?
The integral of 1/(cos(8x)) is 1/8 ln|tan(8x)+sec(8x)|+C