What is the integral from 1 to 4 of (xln(2)-3/(2x)) ?

The integral from 1 to 4 of (xln(2)-3/(2x)) is 9/2 ln(2)

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integral from 1 to 4 of (xln(2)-3/(2x))

\int_{1}^{4} (x ln (2) - \frac{3}{2 x}) d x

\frac{9}{2} ln (2)

Decimal

3.11916 \dots

Solution steps

\int_{1}^{4} x ln (2) - \frac{3}{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} x ln (2) d x - \int_{1}^{4} \frac{3}{2 x} d x

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

\int_{1}^{4} \frac{3}{2 x} d x = 3 ln (2)

= ln (2) \frac{15}{2} - 3 ln (2)

Simplify

ln (2) \frac{15}{2} - 3 ln (2) : \frac{9}{2} ln (2)

= \frac{9}{2} ln (2)

What is the integral from 1 to 4 of (xln(2)-3/(2x)) ?
The integral from 1 to 4 of (xln(2)-3/(2x)) is 9/2 ln(2)