What is the integral from 1 to 4 of (2x+1/x) ?

The integral from 1 to 4 of (2x+1/x) is 15+2ln(2)

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integral from 1 to 4 of (2x+1/x)

\int_{1}^{4} (2 x + \frac{1}{x}) d x

15 + 2 ln (2)

Solution steps

\int_{1}^{4} 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}^{4} 2 x d x + \int_{1}^{4} \frac{1}{x} d x

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} \frac{1}{x} d x = 2 ln (2)

= 15 + 2 ln (2)

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What is the integral from 1 to 4 of (2x+1/x) ?
The integral from 1 to 4 of (2x+1/x) is 15+2ln(2)