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

The integral of (2x+1)/(x^2-3x+2) is -3ln|x-1|+5ln|x-2|+C

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

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

- 3 ln ∣ x - 1 ∣ + 5 ln ∣ x - 2 ∣ + C

Solution steps

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

Take the partial fraction of

\frac{2 x + 1}{x ^{2} - 3 x + 2} : - \frac{3}{x - 1} + \frac{5}{x - 2}

= \int - \frac{3}{x - 1} + \frac{5}{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{3}{x - 1} d x + \int \frac{5}{x - 2} d x

\int \frac{3}{x - 1} d x = 3 ln ∣ x - 1 ∣

\int \frac{5}{x - 2} d x = 5 ln ∣ x - 2 ∣

= - 3 ln ∣ x - 1 ∣ + 5 ln ∣ x - 2 ∣

Add a constant to the solution

= - 3 ln ∣ x - 1 ∣ + 5 ln ∣ x - 2 ∣ + C

y^{^{''}} + 4 y = e - t

y^{^{''}} - 2 y^{^{'}} = 6 e^{2 x}

\int \frac{9 x ^{2} + 6 x + 9}{x ^{3} - 1} d x

e^{2 t} sin (2 t j)

What is the integral of (2x+1)/(x^2-3x+2) ?
The integral of (2x+1)/(x^2-3x+2) is -3ln|x-1|+5ln|x-2|+C