A) \[{{\left( 1+{{x}^{\frac{3}{4}}} \right)}^{\frac{5}{6}}}+c\]
B) \[{{\left( 1+{{x}^{\frac{4}{3}}} \right)}^{\frac{5}{6}}}+c\]
C) \[\frac{5}{8}{{\left( 1+{{x}^{\frac{4}{3}}} \right)}^{\frac{6}{5}}}+c\]
D) \[\frac{1}{6}{{\left( 1+{{x}^{\frac{4}{3}}} \right)}^{6}}+c\]
E) \[\frac{15}{8}{{\left( 1+{{x}^{\frac{4}{3}}} \right)}^{\frac{6}{5}}}+c\]
Correct Answer: C
Solution :
Let\[I=\int{\sqrt[3]{x}}(\sqrt[5]{1+\sqrt[3]{{{x}^{4}}}})dx\] Put \[\sqrt[3]{{{x}^{4}}}=t\] \[\Rightarrow \] \[\frac{4}{3}.\sqrt[3]{x}dx=dt\] \[\therefore \] \[I=\frac{3}{4}\int{(\sqrt[5]{1+t})dt}\] \[=\frac{3}{4}\left[ \frac{{{(1+t)}^{\frac{1}{5}+1}}}{\frac{1}{5}+1} \right]+c\] \[=\frac{5}{8}[{{(1+\sqrt[3]{{{x}^{4}}})}^{6/5}}]+c\]
You need to login to perform this action.
You will be redirected in
3 sec
