What is the integral of sqrt((x^2-2)/(x^8)) ?

The integral of sqrt((x^2-2)/(x^8)) is -(sqrt(x^2-2))/(3x^3)+(sqrt(x^2-2))/(6x)+C

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integral of sqrt((x^2-2)/(x^8))

\int \frac{x ^{2} - 2}{x ^{8}} d x

- \frac{x ^{2} - 2}{3 x ^{3}} + \frac{x ^{2} - 2}{6 x} + C

Solution steps

\int \frac{x ^{2} - 2}{x ^{8}} d x

Simplify

\frac{x ^{2} - 2}{x ^{8}} : \frac{x ^{2} - 2}{x ^{4}}

= \int \frac{x ^{2} - 2}{x ^{4}} d x

Apply Integration By Parts

: - \frac{x ^{2} - 2}{3 x ^{3}} - \int - \frac{1}{3 x ^{2} x ^{2} - 2} d x

= - \frac{x ^{2} - 2}{3 x ^{3}} - \int - \frac{1}{3 x ^{2} x ^{2} - 2} d x

\int - \frac{1}{3 x ^{2} x ^{2} - 2} d x = - \frac{x ^{2} - 2}{6 x}

= - \frac{x ^{2} - 2}{3 x ^{3}} - (- \frac{x ^{2} - 2}{6 x})

Simplify

= - \frac{x ^{2} - 2}{3 x ^{3}} + \frac{x ^{2} - 2}{6 x}

Add a constant to the solution

= - \frac{x ^{2} - 2}{3 x ^{3}} + \frac{x ^{2} - 2}{6 x} + C

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What is the integral of sqrt((x^2-2)/(x^8)) ?
The integral of sqrt((x^2-2)/(x^8)) is -(sqrt(x^2-2))/(3x^3)+(sqrt(x^2-2))/(6x)+C