What is the integral of (2x+3)/(x^2+3x+1) ?

The integral of (2x+3)/(x^2+3x+1) is ln|x^2+3x+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x+3)/(x^2+3x+1)

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

ln x^{2} + 3 x + 1 + C

Solution steps

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

= ln x^{2} + 3 x + 1

Add a constant to the solution

= ln x^{2} + 3 x + 1 + C

\int (7 x + 2)^{4} d x

\int \frac{1}{2 x 1 - 9 x ^{2}} d x

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

\int \frac{2000}{400 q} d q

\int \frac{1}{( 3 x + 4 ) ^{4}} d x

What is the integral of (2x+3)/(x^2+3x+1) ?
The integral of (2x+3)/(x^2+3x+1) is ln|x^2+3x+1|+C