What is the integral from 1 to 3 of e^x-1/x ?

The integral from 1 to 3 of e^x-1/x is e^3-e-ln(3)

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integral from 1 to 3 of e^x-1/x

\int_{1}^{3} e^{x} - \frac{1}{x} d x

e^{3} - e - ln (3)

Solution steps

\int_{1}^{3} 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}^{3} e^{x} d x - \int_{1}^{3} \frac{1}{x} d x

\int_{1}^{3} e^{x} d x = e^{3} - e

\int_{1}^{3} \frac{1}{x} d x = ln (3)

= e^{3} - e - ln (3)

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What is the integral from 1 to 3 of e^x-1/x ?
The integral from 1 to 3 of e^x-1/x is e^3-e-ln(3)