What is the integral of 5/(xln(x^3)) ?

The integral of 5/(xln(x^3)) is 5/3 ln(3|ln(x)|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 5/(xln(x^3))

\int \frac{5}{x ln ( x ^{3} )} d x

\frac{5}{3} ln (3 ∣ ln (x) ∣) + C

Solution steps

\int \frac{5}{x ln ( x ^{3} )} 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 ( x ^{3} )} d x

Apply u-substitution

= 5 \cdot \int \frac{1}{3 u ln ( u )} d u

Take the constant out:

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

= 5 \cdot \frac{1}{3} \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

= 5 \cdot \frac{1}{3} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 5 \cdot \frac{1}{3} ln ∣ v ∣

Substitute back

= 5 \cdot \frac{1}{3} ln ln (x^{3})

Simplify

5 \cdot \frac{1}{3} ln ln (x^{3}) : \frac{5}{3} ln (3 ∣ ln (x) ∣)

= \frac{5}{3} ln (3 ∣ ln (x) ∣)

Add a constant to the solution

= \frac{5}{3} ln (3 ∣ ln (x) ∣) + C

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

\int x x + \frac{1}{x ^{3}} d x

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

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

\int 16 x tan (4 x^{2} + 1) d x

What is the integral of 5/(xln(x^3)) ?
The integral of 5/(xln(x^3)) is 5/3 ln(3|ln(x)|)+C