The value of the integral ∫(x2−1)dxx3(√2x4−2x2+1) is:
A
2√2−2x2+1x4+c
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B
2√2+2x2+1x4+c
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C
12√2−2x2+1x4+c
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D
None of these
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Solution
The correct option is C12√2−2x2+1x4+c I=∫(x2−1)dxx3(√2x4−2x2+1)⇒I=∫x2−1x5√2−2x2+1X4dx⇒I=∫1x3−1x5√2−2x2+1X4dxPut 2−2x2+1X4=t⇒(1x3−1x5)dx=dt4⇒I=14∫dt√t⇒I=12√t+c⇒I=12√2−2x2+1x4+c