What is the integral from 1 to e of (8x-5/x) ?

The integral from 1 to e of (8x-5/x) is 4e^2-9

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integral from 1 to e of (8x-5/x)

\int_{1}^{e} (8 x - \frac{5}{x}) d x

4 e^{2} - 9

Decimal Notation

20.55622 \dots

Solution steps

\int_{1}^{e} 8 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}^{e} 8 x d x - \int_{1}^{e} \frac{5}{x} d x

\int_{1}^{e} 8 x d x = 4 (e^{2} - 1)

\int_{1}^{e} \frac{5}{x} d x = 5

= 4 (e^{2} - 1) - 5

Simplify

4 (e^{2} - 1) - 5 : 4 e^{2} - 9

= 4 e^{2} - 9

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What is the integral from 1 to e of (8x-5/x) ?
The integral from 1 to e of (8x-5/x) is 4e^2-9