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Evaluate: int(dx)/(x^2(x^4+1)^(3/4)) (A)...

Evaluate: `int(dx)/(x^2(x^4+1)^(3/4))` (A) `- ( 1 + 1/x^4)^(1/4) + c` (B) ` ( 1 + 1/x^4)^(1/4) + c` (C) `- ( 1 - 1/x^4)^(1/4) + c` (D) `- ( 1 +1/x^4)^(1/4) + c`

Text Solution

Verified by Experts

Given,`int(dx)/(x^2(x^4+1)^(3/4))`
`int(dx)/(x^5(1+1/x^4)^(3/4))`
Let,`1+1/x^4=t`
`dt=−4/x^5​dx`
`I=−1/4​∫dt/(t^(3/4))`
​ `I=−t^(1/4)+C `
⇒`I=−((x^4+1​)/(x^4))^(1/4)​+C`
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