What is the integral from 1 to 2 of (2+3sqrt(x))/x ?

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

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integral from 1 to 2 of (2+3sqrt(x))/x

\int_{1}^{2} \frac{2 + 3 x}{x} d x

2 ln (2) + 3 (22 - 2)

Decimal Notation

3.87157 \dots

Solution steps

\int_{1}^{2} \frac{2 + 3 x}{x} d x

Expand

\frac{2 + 3 x}{x} : \frac{2}{x} + \frac{3}{x}

= \int_{1}^{2} \frac{2}{x} + \frac{3}{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}^{2} \frac{2}{x} d x + \int_{1}^{2} \frac{3}{x} d x

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

\int_{1}^{2} \frac{3}{x} d x = 3 (22 - 2)

= 2 ln (2) + 3 (22 - 2)

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