A) \[\frac{1}{16}(4{{x}^{4}}\log x-{{x}^{4}}+c)\]
B) \[\frac{1}{8}({{x}^{4}}\log x-4{{x}^{4}}+c)\]
C) \[\frac{1}{16}(4{{x}^{4}}\log x+{{x}^{4}}+c)\]
D) \[\frac{{{x}^{4}}\log x}{4}+c\]
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{{{x}^{3}}\log x\,dx=\log x\frac{{{x}^{4}}}{4}-\int_{{}}^{{}}{\frac{1}{x}.\frac{{{x}^{4}}}{4}}}\] \[=\log x\frac{{{x}^{4}}}{4}-\frac{1}{4}\int_{{}}^{{}}{{{x}^{3}}\,dx}\] \[\frac{{{x}^{4}}\log x}{4}-\frac{1}{4}.\frac{{{x}^{4}}}{4}+c\] \[=\frac{1}{16}(4{{x}^{4}}\log x-{{x}^{4}}+c)\]
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