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

The integral from 1 to 2 of (4/(x^2)+1) is 3

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

\int_{1}^{2} (\frac{4}{x ^{2}} + 1) d x

3

Solution steps

\int_{1}^{2} \frac{4}{x ^{2}} + 1 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{4}{x ^{2}} d x + \int_{1}^{2} 1 d x

\int_{1}^{2} \frac{4}{x ^{2}} d x = 2

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

= 2 + 1

Simplify

= 3

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What is the integral from 1 to 2 of (4/(x^2)+1) ?
The integral from 1 to 2 of (4/(x^2)+1) is 3