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

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

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

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

\frac{3}{2} - ln (2)

Decimal

0.80685 \dots

Solution steps

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

Expand

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

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

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

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

= \frac{3}{2} - ln (2)

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