What is the integral of (2x-5)/(x^2-5x+6) ?

The integral of (2x-5)/(x^2-5x+6) is ln|x^2-5x+6|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x-5)/(x^2-5x+6)

\int \frac{2 x - 5}{x ^{2} - 5 x + 6} d x

ln x^{2} - 5 x + 6 + C

Solution steps

\int \frac{2 x - 5}{x ^{2} - 5 x + 6} 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} - 5 x + 6

= ln x^{2} - 5 x + 6

Add a constant to the solution

= ln x^{2} - 5 x + 6 + C

\int_{12}^{\infty} x e^{- x} d x

f (x) = sin (e^{x})

f (x)

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

\frac{\partial}{\partial x} (e^{- \frac{x ^{2}}{6} - \frac{y ^{2}}{6}})

What is the integral of (2x-5)/(x^2-5x+6) ?
The integral of (2x-5)/(x^2-5x+6) is ln|x^2-5x+6|+C