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

The integral from-1 to 1 of x-3+1/(x-2) is -ln(3)-6

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

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

- ln (3) - 6

Decimal

- 7.09861 \dots

Solution steps

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

\int_{- 1}^{1} x d x = 0

\int_{- 1}^{1} 3 d x = 6

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

= 0 - 6 - ln (3)

Simplify

= - ln (3) - 6

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What is the integral from-1 to 1 of x-3+1/(x-2) ?
The integral from-1 to 1 of x-3+1/(x-2) is -ln(3)-6