What is the integral from 1/2 to 3/2 of (x+1/x) ?

The integral from 1/2 to 3/2 of (x+1/x) is 1+ln(3)

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integral from 1/2 to 3/2 of (x+1/x)

\int_{\frac{1}{2}}^{\frac{3}{2}} (x + \frac{1}{x}) d x

1 + ln (3)

Decimal Notation

2.09861 \dots

Solution steps

\int_{\frac{1}{2}}^{\frac{3}{2}} 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_{\frac{1}{2}}^{\frac{3}{2}} x d x + \int_{\frac{1}{2}}^{\frac{3}{2}} \frac{1}{x} d x

\int_{\frac{1}{2}}^{\frac{3}{2}} x d x = 1

\int_{\frac{1}{2}}^{\frac{3}{2}} \frac{1}{x} d x = ln (3)

= 1 + ln (3)

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What is the integral from 1/2 to 3/2 of (x+1/x) ?
The integral from 1/2 to 3/2 of (x+1/x) is 1+ln(3)