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

The integral from 2 to 3 of (4/(x^2)-3)^2 is 443/81

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

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

\frac{443}{81}

Decimal Notation

5.46913 \dots

Solution steps

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

Expand

(\frac{4}{x ^{2}} - 3)^{2} : \frac{16}{x ^{4}} - \frac{24}{x ^{2}} + 9

= \int_{2}^{3} \frac{16}{x ^{4}} - \frac{24}{x ^{2}} + 9 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}^{3} \frac{16}{x ^{4}} d x - \int_{2}^{3} \frac{24}{x ^{2}} d x + \int_{2}^{3} 9 d x

\int_{2}^{3} \frac{16}{x ^{4}} d x = \frac{38}{81}

\int_{2}^{3} \frac{24}{x ^{2}} d x = 4

\int_{2}^{3} 9 d x = 9

= \frac{38}{81} - 4 + 9

Simplify

\frac{38}{81} - 4 + 9 : \frac{443}{81}

= \frac{443}{81}

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What is the integral from 2 to 3 of (4/(x^2)-3)^2 ?
The integral from 2 to 3 of (4/(x^2)-3)^2 is 443/81