What is the integral from 1/2 to 4 of 2/x-1/8 x ?

The integral from 1/2 to 4 of 2/x-1/8 x is 6ln(2)-63/64

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integral from 1/2 to 4 of 2/x-1/8 x

\int_{\frac{1}{2}}^{4} \frac{2}{x} - \frac{1}{8} x d x

6 ln (2) - \frac{63}{64}

Decimal Notation

3.17450 \dots

Solution steps

\int_{\frac{1}{2}}^{4} \frac{2}{x} - \frac{1}{8} 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}}^{4} \frac{2}{x} d x - \int_{\frac{1}{2}}^{4} \frac{1}{8} x d x

\int_{\frac{1}{2}}^{4} \frac{2}{x} d x = 6 ln (2)

\int_{\frac{1}{2}}^{4} \frac{1}{8} x d x = \frac{63}{64}

= 6 ln (2) - \frac{63}{64}

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\frac{d}{d x} (\frac{2 x}{2 + x ^{2}})

What is the integral from 1/2 to 4 of 2/x-1/8 x ?
The integral from 1/2 to 4 of 2/x-1/8 x is 6ln(2)-63/64