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 :
\[I=\int{\frac{dx}{{{x}^{6}}{{(1+{{x}^{-5}})}^{4/5}}}}\] \[=\int{\frac{{{x}^{-\,6}}dx}{{{(1+{{x}^{-\,5}})}^{4/5}}}}\] \[put\,{{x}^{-5}}=t\] \[\frac{-\,5}{{{x}^{6}}}dx=dt\] \[=\frac{-1}{5}\int{\frac{dt}{{{(1+t)}^{4/5}}}}=-\frac{1}{5}{{(1+t)}^{1/5}}+c\] \[=-\frac{1}{5}{{(1+{{x}^{-5}})}^{1/5}}+c\]
You need to login to perform this action.
You will be redirected in
3 sec
