What is the integral from 1/2 to 3 of 3/x-1/3 x ?

The integral from 1/2 to 3 of 3/x-1/3 x is 3ln(6)-35/24

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integral from 1/2 to 3 of 3/x-1/3 x

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

3 ln (6) - \frac{35}{24}

Decimal

3.91694 \dots

Solution steps

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

\int_{\frac{1}{2}}^{3} \frac{3}{x} d x = 3 ln (6)

\int_{\frac{1}{2}}^{3} \frac{1}{3} x d x = \frac{35}{24}

= 3 ln (6) - \frac{35}{24}

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What is the integral from 1/2 to 3 of 3/x-1/3 x ?
The integral from 1/2 to 3 of 3/x-1/3 x is 3ln(6)-35/24