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}

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}

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

\int_{0}^{4} 16 x - x^{3} d x

\int_{0}^{5} (x^{2} - x + 1) e^{2 x} d x

\int_{0}^{6} ∣ x - 5 ∣ d x

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

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