What is the integral from 1 to 5 of (2x+1/x) ?

The integral from 1 to 5 of (2x+1/x) is 24+ln(5)

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integral from 1 to 5 of (2x+1/x)

\int_{1}^{5} (2 x + \frac{1}{x}) d x

24 + ln (5)

Decimal

25.60943 \dots

Solution steps

\int_{1}^{5} 2 x + \frac{1}{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}^{5} 2 x d x + \int_{1}^{5} \frac{1}{x} d x

\int_{1}^{5} 2 x d x = 24

\int_{1}^{5} \frac{1}{x} d x = ln (5)

= 24 + ln (5)

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What is the integral from 1 to 5 of (2x+1/x) ?
The integral from 1 to 5 of (2x+1/x) is 24+ln(5)