What is the integral from-2 to 2 of (32)/(x^2+4)-x^2 ?

The integral from-2 to 2 of (32)/(x^2+4)-x^2 is 8pi-16/3

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integral from-2 to 2 of (32)/(x^2+4)-x^2

\int_{- 2}^{2} \frac{32}{x ^{2} + 4} - x^{2} d x

8 π - \frac{16}{3}

Decimal Notation

19.79940 \dots

Solution steps

\int_{- 2}^{2} \frac{32}{x ^{2} + 4} - x^{2} 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_{- 2}^{2} \frac{32}{x ^{2} + 4} d x - \int_{- 2}^{2} x^{2} d x

\int_{- 2}^{2} \frac{32}{x ^{2} + 4} d x = 8 π

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

= 8 π - \frac{16}{3}

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What is the integral from-2 to 2 of (32)/(x^2+4)-x^2 ?
The integral from-2 to 2 of (32)/(x^2+4)-x^2 is 8pi-16/3