What is the integral from 1 to 4 of (x/2-5/x) ?

The integral from 1 to 4 of (x/2-5/x) is 15/4-10ln(2)

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integral from 1 to 4 of (x/2-5/x)

\int_{1}^{4} (\frac{x}{2} - \frac{5}{x}) d x

\frac{15}{4} - 10 ln (2)

Decimal Notation

- 3.18147 \dots

Solution steps

\int_{1}^{4} \frac{x}{2} - \frac{5}{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{5}{x} d x

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

\int_{1}^{4} \frac{5}{x} d x = 10 ln (2)

= \frac{15}{4} - 10 ln (2)

x \to \frac{7}{8} lim (x^{4})

\frac{d}{d x} (\frac{e ^{x - 2}}{x})

\int \frac{2 x}{9 - 4 x ^{2}} d x

\frac{d}{d x} (2 - 2 sin (x))

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

What is the integral from 1 to 4 of (x/2-5/x) ?
The integral from 1 to 4 of (x/2-5/x) is 15/4-10ln(2)