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

The integral from 1 to 4 of x-3ln(x)-2/x is -28ln(2)+33/2

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

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

- 28 ln (2) + \frac{33}{2}

Decimal

- 2.90812 \dots

Solution steps

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

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

\int_{1}^{4} 3 ln (x) d x = 3 (8 ln (2) - 3)

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

= \frac{15}{2} - 3 (8 ln (2) - 3) - 4 ln (2)

Simplify

\frac{15}{2} - 3 (8 ln (2) - 3) - 4 ln (2) : - 28 ln (2) + \frac{33}{2}

= - 28 ln (2) + \frac{33}{2}

What is the integral from 1 to 4 of x-3ln(x)-2/x ?
The integral from 1 to 4 of x-3ln(x)-2/x is -28ln(2)+33/2