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$\int x^{- 11} {(1 + x^{4})}^{- 1 / 2} d x is equal to$

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12t55+2t33+t+c, where t=1+1x4

-12t55-2t33+t+c, where t=1+1x4

t55-2t33+t+c, where t=1+1x4

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detailed solution

Correct option is B

Let I=∫dxx111+x41/2=∫dxx11⋅x21+1/x41/2Let 1+1x4=t2 . Then −4x5dx=2tdt⇒ I=∫dxx131+1/x41/2 =−14∫2tdtx8t =−12∫t2−12dt =−12∫t4−2t2+1dt =−12t55−2t33+t+c, where t=1+1x4

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∫x−111+x4−1/2dx is equal to

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$\int x^{- 11} {(1 + x^{4})}^{- 1 / 2} d x is equal to$