What is the integral from 1 to 5 of (4x-4/x) ?

The integral from 1 to 5 of (4x-4/x) is 48-4ln(5)

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integral from 1 to 5 of (4x-4/x)

\int_{1}^{5} (4 x - \frac{4}{x}) d x

48 - 4 ln (5)

Decimal

41.56224 \dots

Solution steps

\int_{1}^{5} 4 x - \frac{4}{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} 4 x d x - \int_{1}^{5} \frac{4}{x} d x

\int_{1}^{5} 4 x d x = 48

\int_{1}^{5} \frac{4}{x} d x = 4 ln (5)

= 48 - 4 ln (5)

What is the integral from 1 to 5 of (4x-4/x) ?
The integral from 1 to 5 of (4x-4/x) is 48-4ln(5)