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

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

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

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

- 2 ln ∣ x - 1 ∣ + 3 ln ∣ x - 2 ∣ + C

Solution steps

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

Take the partial fraction of

\frac{x + 1}{x ^{2} - 3 x + 2} : - \frac{2}{x - 1} + \frac{3}{x - 2}

= \int - \frac{2}{x - 1} + \frac{3}{x - 2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{2}{x - 1} d x + \int \frac{3}{x - 2} d x

\int \frac{2}{x - 1} d x = 2 ln ∣ x - 1 ∣

\int \frac{3}{x - 2} d x = 3 ln ∣ x - 2 ∣

= - 2 ln ∣ x - 1 ∣ + 3 ln ∣ x - 2 ∣

Add a constant to the solution

= - 2 ln ∣ x - 1 ∣ + 3 ln ∣ x - 2 ∣ + C

x - 2 x^{2}

\frac{d ^{3}}{d x ^{3}} (e^{5 x - 4})

n = 1 \sum \infty \frac{n !}{9 0 ^{n}}

x \to 2 lim (2 x^{3} - x^{2} + 7 x - 3)

\frac{d}{d x} (2 tan (x) sec (x))

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