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)

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)

\int_{2}^{10} (5 x^{2} - 2) d x

\int_{0}^{1} x^{4} - 1 d x

\int_{0.1}^{3} ln (x) d x

\int_{- 3}^{3} x^{5} d x

\int_{0}^{5} \frac{3}{5 - x} d x

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)