What is the integral from 2 to 5 of (y^2-1/(y^2))^2 ?

The integral from 2 to 5 of (y^2-1/(y^2))^2 is 612639/1000

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integral from 2 to 5 of (y^2-1/(y^2))^2

\int_{2}^{5} (y^{2} - \frac{1}{y ^{2}})^{2} d y

\frac{612639}{1000}

Decimal

612.639

Solution steps

\int_{2}^{5} (y^{2} - \frac{1}{y ^{2}})^{2} d y

Expand

(y^{2} - \frac{1}{y ^{2}})^{2} : y^{4} - 2 + \frac{1}{y ^{4}}

= \int_{2}^{5} y^{4} - 2 + \frac{1}{y ^{4}} d y

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}^{5} y^{4} d y - \int_{2}^{5} 2 d y + \int_{2}^{5} \frac{1}{y ^{4}} d y

\int_{2}^{5} y^{4} d y = \frac{3093}{5}

\int_{2}^{5} 2 d y = 6

\int_{2}^{5} \frac{1}{y ^{4}} d y = \frac{39}{1000}

= \frac{3093}{5} - 6 + \frac{39}{1000}

Simplify

\frac{3093}{5} - 6 + \frac{39}{1000} : \frac{612639}{1000}

= \frac{612639}{1000}

What is the integral from 2 to 5 of (y^2-1/(y^2))^2 ?
The integral from 2 to 5 of (y^2-1/(y^2))^2 is 612639/1000