What is the integral of pi/(xln(x)) ?

The integral of pi/(xln(x)) is piln|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 pi/(xln(x))

\int \frac{π}{x ln ( x )} d x

π ln ∣ ln (x) ∣ + C

Solution steps

\int \frac{π}{x ln ( x )} d x

Take the constant out:

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

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

Apply u-substitution

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

= π \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= π ln ∣ u ∣

Substitute back

u = ln (x)

= π ln ∣ ln (x) ∣

Add a constant to the solution

= π ln ∣ ln (x) ∣ + C

\int \frac{3 x}{2} - \frac{9}{4 x} + 2 d x

\int 5 (x^{4} + 5)^{5} d x

\int (e^{2 x} - 1) d x

\int - \frac{12}{x ^{4}} d x

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

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