What is the integral from 1 to 5 of 5/x-3/(x^2) ?

The integral from 1 to 5 of 5/x-3/(x^2) is 5ln(5)-12/5

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integral from 1 to 5 of 5/x-3/(x^2)

\int_{1}^{5} \frac{5}{x} - \frac{3}{x ^{2}} d x

5 ln (5) - \frac{12}{5}

Decimal

5.64718 \dots

Solution steps

\int_{1}^{5} \frac{5}{x} - \frac{3}{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} \frac{5}{x} d x - \int_{1}^{5} \frac{3}{x ^{2}} d x

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

\int_{1}^{5} \frac{3}{x ^{2}} d x = \frac{12}{5}

= 5 ln (5) - \frac{12}{5}

What is the integral from 1 to 5 of 5/x-3/(x^2) ?
The integral from 1 to 5 of 5/x-3/(x^2) is 5ln(5)-12/5