A) \[{{(3+5{{x}^{4}})}^{3/2}}+c\]
B) \[\frac{1}{5}{{(3+5{{x}^{4}})}^{3/2}}+c\]
C) \[\frac{1}{30}{{(3+5{{x}^{4}})}^{3/2}}+c\]
D) None of these
Correct Answer: C
Solution :
Put \[3+5{{x}^{4}}=t\Rightarrow 20{{x}^{3}}dx=dt,\] then \[\int_{{}}^{{}}{{{x}^{3}}\sqrt{3+5{{x}^{4}}}dx}=\frac{1}{20}\int_{{}}^{{}}{{{t}^{1/2}}dt}\] \[=\frac{2}{3}\times \frac{1}{20}.{{t}^{3/2}}+c=\frac{1}{30}{{(3+5{{x}^{4}})}^{3/2}}+c.\]
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