What is the integral from 1 to 9 of 2x+1/x ?

The integral from 1 to 9 of 2x+1/x is 80+2ln(3)

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integral from 1 to 9 of 2x+1/x

\int_{1}^{9} 2 x + \frac{1}{x} d x

80 + 2 ln (3)

Solution steps

\int_{1}^{9} 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}^{9} 2 x d x + \int_{1}^{9} \frac{1}{x} d x

\int_{1}^{9} 2 x d x = 80

\int_{1}^{9} \frac{1}{x} d x = 2 ln (3)

= 80 + 2 ln (3)

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What is the integral from 1 to 9 of 2x+1/x ?
The integral from 1 to 9 of 2x+1/x is 80+2ln(3)