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

The integral from 1 to 3 of (2x+2/x) is 8+2ln(3)

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

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

8 + 2 ln (3)

Decimal Notation

10.19722 \dots

Solution steps

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

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

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

= 8 + 2 ln (3)

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What is the integral from 1 to 3 of (2x+2/x) ?
The integral from 1 to 3 of (2x+2/x) is 8+2ln(3)