What is the integral from 1 to 5 of (5+1/x+e^x) ?

The integral from 1 to 5 of (5+1/x+e^x) is 20+ln(5)+e^5-e

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integral from 1 to 5 of (5+1/x+e^x)

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

20 + ln (5) + e^{5} - e

Decimal

167.30431 \dots

Solution steps

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

\int_{1}^{5} 5 d x = 20

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

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

= 20 + ln (5) + e^{5} - e

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What is the integral from 1 to 5 of (5+1/x+e^x) ?
The integral from 1 to 5 of (5+1/x+e^x) is 20+ln(5)+e^5-e