What is the integral of (2x+9)/(x^2+9x+3) ?

The integral of (2x+9)/(x^2+9x+3) is ln|x^2+9x+3|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x+9)/(x^2+9x+3)

\int \frac{2 x + 9}{x ^{2} + 9 x + 3} d x

ln x^{2} + 9 x + 3 + C

Solution steps

\int \frac{2 x + 9}{x ^{2} + 9 x + 3} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{2} + 9 x + 3

= ln x^{2} + 9 x + 3

Add a constant to the solution

= ln x^{2} + 9 x + 3 + C

\int \frac{16 - x ^{2}}{x} d x

\int \frac{2 x - 3}{x ^{2} - 2 x + 5} d x

\int 16 - x^{2} - y^{2} d x

\int 2 tan^{2} (2 x) d x

\int (1 + tan^{2} (a)) d a

What is the integral of (2x+9)/(x^2+9x+3) ?
The integral of (2x+9)/(x^2+9x+3) is ln|x^2+9x+3|+C