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Evaluate: int(x^2)/(x^6-a^6)dx...

Evaluate: `int(x^2)/(x^6-a^6)dx`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(3)(1)/(2a^(3))"log"_(e)|(x^(3)-a^(3))/(x^(3)+a^(3))|+C`
`I=int(x^(2))/(x^(6)-a^(6))dx`
` "let "x^(3)=t`
` :. 3x^(2)dx=dt`
` :. I=(1)/(3)int(dt)/(t^(2)-a^(6))=(1)/(3)(1)/(2a^(3))"log"_(e)|(t-a^(3))/(t+a^(3))|+C`
`=(1)/(3)(1)/(2a^(3))"log"_(e)|(x^(3)-a^(3))/(x^(3)+a^(3))|+C`
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