What is the integral from-1 to 0 of (3-x)/(x^2-3x+2) ?

The integral from-1 to 0 of (3-x)/(x^2-3x+2) is -3ln(3/4)-(-ln(3)-3ln(3/4))/2

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integral from-1 to 0 of (3-x)/(x^2-3x+2)

\int_{- 1}^{0} \frac{3 - x}{x ^{2} - 3 x + 2} d x

- 3 ln (\frac{3}{4}) - \frac{- ln ( 3 ) - 3 ln ( \frac{3}{4} )}{2}

Decimal

0.98082 \dots

Solution steps

\int_{- 1}^{0} \frac{3 - x}{x ^{2} - 3 x + 2} d x

Expand

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

Apply the Sum Rule:

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

= \int_{- 1}^{0} \frac{3}{x ^{2} - 3 x + 2} d x - \int_{- 1}^{0} \frac{x}{x ^{2} - 3 x + 2} d x

\int_{- 1}^{0} \frac{3}{x ^{2} - 3 x + 2} d x = - 3 ln (\frac{3}{4})

\int_{- 1}^{0} \frac{x}{x ^{2} - 3 x + 2} d x = \frac{- ln ( 3 ) - 3 ln ( \frac{3}{4} )}{2}

= - 3 ln (\frac{3}{4}) - \frac{- ln ( 3 ) - 3 ln ( \frac{3}{4} )}{2}

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What is the integral from-1 to 0 of (3-x)/(x^2-3x+2) ?
The integral from-1 to 0 of (3-x)/(x^2-3x+2) is -3ln(3/4)-(-ln(3)-3ln(3/4))/2