Correct option is 127log⁡x7/2+x7+1+c

Questions

$\int \frac{x^{5 / 2}}{\sqrt{1 + x^{7}}} d x is$

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27log⁡x7/2+x7+1+c

12log⁡x7+1x7−1+c

21+x7+c

None of these

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detailed solution

Correct option is A

Put x7/2=t∴72x5/2dx=dt∴I=∫27dt1+t2=27log⁡t+1+t2+k=27log⁡x7/2+1+x7+k

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∫x5/21+x7dx is

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$\int \frac{x^{5 / 2}}{\sqrt{1 + x^{7}}} d x is$