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

The integral from 1 to 5 of (5x-5/x) is 60-5ln(5)

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integral from 1 to 5 of (5x-5/x)

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

60 - 5 ln (5)

Decimal

51.95281 \dots

Solution steps

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

\int_{1}^{5} 5 x d x = 60

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

= 60 - 5 ln (5)

What is the integral from 1 to 5 of (5x-5/x) ?
The integral from 1 to 5 of (5x-5/x) is 60-5ln(5)