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

The integral from 1 to 5 of (5x^2-2)/(x^3) is 5ln(5)-24/25

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

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

5 ln (5) - \frac{24}{25}

Decimal

7.08718 \dots

Solution steps

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

Expand

\frac{5 x ^{2} - 2}{x ^{3}} : \frac{5}{x} - \frac{2}{x ^{3}}

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

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

\int_{1}^{5} \frac{2}{x ^{3}} d x = \frac{24}{25}

= 5 ln (5) - \frac{24}{25}

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What is the integral from 1 to 5 of (5x^2-2)/(x^3) ?
The integral from 1 to 5 of (5x^2-2)/(x^3) is 5ln(5)-24/25