What is the integral from 8 to 16 of (x+1/x) ?

The integral from 8 to 16 of (x+1/x) is 96+ln(2)

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integral from 8 to 16 of (x+1/x)

\int_{8}^{16} (x + \frac{1}{x}) d x

96 + ln (2)

Decimal Notation

96.69314 \dots

Solution steps

\int_{8}^{16} 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_{8}^{16} x d x + \int_{8}^{16} \frac{1}{x} d x

\int_{8}^{16} x d x = 96

\int_{8}^{16} \frac{1}{x} d x = ln (2)

= 96 + ln (2)

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What is the integral from 8 to 16 of (x+1/x) ?
The integral from 8 to 16 of (x+1/x) is 96+ln(2)