What is the integral of 5/(xln(4x)) ?

The integral of 5/(xln(4x)) is 5ln|ln(4x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/(xln(4x))

\int \frac{5}{x ln ( 4 x )} d x

5 ln ∣ ln (4 x) ∣ + C

Solution steps

\int \frac{5}{x ln ( 4 x )} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{x ln ( 4 x )} d x

Apply u-substitution

: \int \frac{1}{u ln ( u )} d u

= 5 \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= 5 \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 5 ln ∣ v ∣

Substitute back

= 5 ln ∣ ln (4 x) ∣

Add a constant to the solution

= 5 ln ∣ ln (4 x) ∣ + C

\frac{d}{d x} (- 4 e^{- 4 x})

\frac{d}{d x} (7 x - 8)

n = 0 \sum \infty (400) (0.1)^{n}

\frac{d y}{d x} = \frac{x ^{2} + 2}{3 y ^{2}}

(x^{2} + x)^{^{'}}

What is the integral of 5/(xln(4x)) ?
The integral of 5/(xln(4x)) is 5ln|ln(4x)|+C