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

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

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integral from 1 to 4 of (e^x)-(1/x)

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

e^{4} - e - 2 ln (2)

Decimal

50.49357 \dots

Solution steps

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

\int_{1}^{4} e^{x} d x = e^{4} - e

\int_{1}^{4} \frac{1}{x} d x = 2 ln (2)

= e^{4} - e - 2 ln (2)

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