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प्रश्न
`intdx/(x^3(1 + x^4)^(1/2))` equals ______.
पर्याय
`-1/(2x^2) sqrt(1 + x^4) + c`
`1/(2x) sqrt(1 + x^4) + c`
`-1/(4x) sqrt(1 + x^4) + c`
`1/(4x^2) sqrt(1 + x^4) + c`
MCQ
रिकाम्या जागा भरा
उत्तर
`intdx/(x^3(1 + x^4)^(1/2))` equals `bbunderline(-1/(2x^2) sqrt(1 + x^4) + c)`.
Explanation:
`intdx/(x^3(1 + x^4)^(1/2)) = intdx/(x^5(1 + 1/x^4)^(1/2)) ...("Let" 1 + x^-4 = 1 + 1/x^4 = t, dt = -4x^-5dx = -4/x^5dx ⇒ dx/x^5 = 1/4dt)`
= `-1/4 intdt/t^(1/2) = -1/4 xx 2 xx sqrtt + c`, where 'c' denotes any arbitrary constant of integration.
= `-1/2 sqrt(1+ 1/x^4) + c`
= `-1/(2x^2) sqrt(1 + x^4) + c`
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