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int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1)...

`int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1))dx` is equal to

A

` 2 sqrt ( 2 - (2)/(x ^ 2 ) + (1)/(x ^4 ) ) + c `

B

` 2 sqrt ( 2 + (2)/(x^2 ) + (1)/(x ^ 4 )) + c `

C

` (1)/(2) sqrt( 2 - (2)/(x ^ 2 ) + (1)/(x ^ 4 ) ) + c `

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the integral \[ \int \frac{x^2 - 1}{x^3 \sqrt{2x^4 - 2x^2 + 1}} \, dx, \] we will follow these steps: ### Step 1: Rewrite the integral We start by rewriting the integral as follows: \[ \int \frac{x^2 - 1}{x^3 \sqrt{2x^4 - 2x^2 + 1}} \, dx = \int \frac{x^2}{x^3 \sqrt{2x^4 - 2x^2 + 1}} \, dx - \int \frac{1}{x^3 \sqrt{2x^4 - 2x^2 + 1}} \, dx. \]
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