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

The integral from 1 to 3 of (x^{-2}-3/x+2x) is -3ln(3)+26/3

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

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

- 3 ln (3) + \frac{26}{3}

Decimal Notation

5.37082 \dots

Solution steps

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

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

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

\int_{1}^{3} 2 x d x = 8

= \frac{2}{3} - 3 ln (3) + 8

Combine the fractions

8 + \frac{2}{3} : \frac{26}{3}

= - 3 ln (3) + \frac{26}{3}

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What is the integral from 1 to 3 of (x^{-2}-3/x+2x) ?
The integral from 1 to 3 of (x^{-2}-3/x+2x) is -3ln(3)+26/3