What is the integral of (2x+1)/(x+x^2) ?

The integral of (2x+1)/(x+x^2) is ln|x+x^2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x+1)/(x+x^2)

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

ln x + x^{2} + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x + x^{2}

= ln x + x^{2}

Add a constant to the solution

= ln x + x^{2} + C

What is the integral of (2x+1)/(x+x^2) ?
The integral of (2x+1)/(x+x^2) is ln|x+x^2|+C