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

The integral from 1 to e of ((x+2))/x is e+1

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integral from 1 to e of ((x+2))/x

\int_{1}^{e} \frac{( x + 2 )}{x} d x

e + 1

Decimal

3.71828 \dots

Solution steps

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

Expand

\frac{x + 2}{x} : 1 + \frac{2}{x}

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

\int_{1}^{e} 1 d x = e - 1

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

= e - 1 + 2

Simplify

= e + 1

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\int_{0}^{\frac{3}{10}} \frac{1}{100 x ^{2} + 9} d x

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