What is the integral from 1 to 2 of (2x+5)/(x^2) ?

The integral from 1 to 2 of (2x+5)/(x^2) is 2ln(2)+5/2

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integral from 1 to 2 of (2x+5)/(x^2)

\int_{1}^{2} \frac{2 x + 5}{x ^{2}} d x

2 ln (2) + \frac{5}{2}

Decimal Notation

3.88629 \dots

Solution steps

\int_{1}^{2} \frac{2 x + 5}{x ^{2}} d x

Expand

\frac{2 x + 5}{x ^{2}} : \frac{2}{x} + \frac{5}{x ^{2}}

= \int_{1}^{2} \frac{2}{x} + \frac{5}{x ^{2}} 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}^{2} \frac{2}{x} d x + \int_{1}^{2} \frac{5}{x ^{2}} d x

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

\int_{1}^{2} \frac{5}{x ^{2}} d x = \frac{5}{2}

= 2 ln (2) + \frac{5}{2}

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What is the integral from 1 to 2 of (2x+5)/(x^2) ?
The integral from 1 to 2 of (2x+5)/(x^2) is 2ln(2)+5/2