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

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

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integral from 1 to e of ((x^2-1))/x

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

\frac{e ^{2} - 1}{2} - 1

Decimal

2.19452 \dots

Solution steps

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

Expand

\frac{x ^{2} - 1}{x} : x - \frac{1}{x}

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

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

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

= \frac{e ^{2} - 1}{2} - 1

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