What is the integral from 1 to 4 of x/2+1/(2x) ?

The integral from 1 to 4 of x/2+1/(2x) is 15/4+ln(2)

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integral from 1 to 4 of x/2+1/(2x)

\int_{1}^{4} \frac{x}{2} + \frac{1}{2 x} d x

\frac{15}{4} + ln (2)

Decimal

4.44314 \dots

Solution steps

\int_{1}^{4} \frac{x}{2} + \frac{1}{2 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}^{4} \frac{x}{2} d x + \int_{1}^{4} \frac{1}{2 x} d x

\int_{1}^{4} \frac{x}{2} d x = \frac{15}{4}

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

= \frac{15}{4} + ln (2)

What is the integral from 1 to 4 of x/2+1/(2x) ?
The integral from 1 to 4 of x/2+1/(2x) is 15/4+ln(2)