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

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

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

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

ln (5) + \frac{24}{5}

Decimal

6.40943 \dots

Solution steps

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

\int_{1}^{5} 1 d x = 4

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

\int_{1}^{5} \frac{1}{x ^{2}} d x = \frac{4}{5}

= 4 + ln (5) + \frac{4}{5}

Combine the fractions

4 + \frac{4}{5} : \frac{24}{5}

= ln (5) + \frac{24}{5}

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