A) \[c+\frac{\sqrt[5]{1+{{x}^{5}}}}{4x}\]
B) \[c-\frac{\sqrt[5]{1+{{x}^{5}}}}{x}\]
C) \[c-\frac{\sqrt[5]{1+{{x}^{5}}}}{5x}\]
D) \[c+\frac{\sqrt[5]{1+{{x}^{5}}}}{x}\]
Correct Answer: B
Solution :
| \[I=\int{\frac{dx}{{{x}^{6}}{{(1+{{x}^{-\,5}})}^{4/5}}}}=\int{\frac{{{x}^{-\,6}}\,\,dx}{{{(1+{{x}^{-\,5}})}^{4/5}}}}\] |
| Put \[{{x}^{-\,5}}=t\] |
| \[\frac{-\,5}{{{x}^{6}}}\,\,dx=dt\] |
| \[\frac{-1}{5}\int{\frac{dt}{{{(1+t)}^{4/5}}}}=-\frac{1}{5}{{(1+t)}^{1/5}}+\] |
| \[c=-\frac{1}{5}{{(1+{{x}^{-\,5}})}^{1/5}}+c\] |
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