What is the integral from-3 to 3 of ((18)/(9+x^2)-1) ?

The integral from-3 to 3 of ((18)/(9+x^2)-1) is 3pi-6

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integral from-3 to 3 of ((18)/(9+x^2)-1)

\int_{- 3}^{3} (\frac{18}{9 + x ^{2}} - 1) d x

3 π - 6

Decimal

3.42477 \dots

Solution steps

\int_{- 3}^{3} \frac{18}{9 + 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_{- 3}^{3} \frac{18}{9 + x ^{2}} d x - \int_{- 3}^{3} 1 d x

\int_{- 3}^{3} \frac{18}{9 + x ^{2}} d x = 3 π

\int_{- 3}^{3} 1 d x = 6

= 3 π - 6

What is the integral from-3 to 3 of ((18)/(9+x^2)-1) ?
The integral from-3 to 3 of ((18)/(9+x^2)-1) is 3pi-6