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

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

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

ln ∣ tan (ln (x)) + sec (ln (x)) ∣ + C

Solution steps

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

Apply u-substitution

: \int sec (u) d u

= \int sec (u) d u

Use the common integral:

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

= ln ∣ tan (u) + sec (u) ∣

Substitute back

u = ln (x)

= ln ∣ tan (ln (x)) + sec (ln (x)) ∣

Add a constant to the solution

= ln ∣ tan (ln (x)) + sec (ln (x)) ∣ + C

\int \frac{10}{x ^{6}} - 2 e^{x} + 3 d x

\int sin (x) cot^{2} (x) d x

\int a x^{- 1} d x

\int \frac{1}{( x + 1 ) ( x + 3 ) ^{2}} d x

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

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