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

The integral from 1 to 3 of (3x^2+4/(x^2)) is 86/3

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

\int_{1}^{3} (3 x^{2} + \frac{4}{x ^{2}}) d x

\frac{86}{3}

Decimal

28.66666 \dots

Solution steps

\int_{1}^{3} 3 x^{2} + \frac{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_{1}^{3} 3 x^{2} d x + \int_{1}^{3} \frac{4}{x ^{2}} d x

\int_{1}^{3} 3 x^{2} d x = 26

\int_{1}^{3} \frac{4}{x ^{2}} d x = \frac{8}{3}

= 26 + \frac{8}{3}

Simplify

26 + \frac{8}{3} : \frac{86}{3}

= \frac{86}{3}

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What is the integral from 1 to 3 of (3x^2+4/(x^2)) ?
The integral from 1 to 3 of (3x^2+4/(x^2)) is 86/3