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

The integral from 1 to 2 of (x+2x^2)/x is 4

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

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

4

Solution steps

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

Expand

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

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

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

= 1 + 3

Simplify

= 4

n = 2 \sum \infty \frac{1}{n + 1}

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What is the integral from 1 to 2 of (x+2x^2)/x ?
The integral from 1 to 2 of (x+2x^2)/x is 4