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

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

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

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

ln (3) + \frac{2}{3}

Solution steps

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

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

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

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

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