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

The integral from 1 to 2 of 2/(x^2)-3x^2-1 is -7

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

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

- 7

Solution steps

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

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

\int_{1}^{2} 3 x^{2} d x = 7

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

= 1 - 7 - 1

Simplify

= - 7

What is the integral from 1 to 2 of 2/(x^2)-3x^2-1 ?
The integral from 1 to 2 of 2/(x^2)-3x^2-1 is -7