A) \[\frac{{{x}^{4}}\log x}{4}+c\]
B) \[\frac{1}{16}[4{{x}^{4}}\log x-{{x}^{4}}]+c\]
C) \[\frac{1}{8}[{{x}^{4}}\log x-4{{x}^{2}}]+c\]
D) \[\frac{1}{16}[4{{x}^{4}}\log x+{{x}^{4}}]+c\]
Correct Answer: B
Solution :
\[I=\int{{{x}^{3}}\log x\,dx}\]\[=\frac{{{x}^{4}}}{4}\log x-\int{\frac{{{x}^{4}}}{4}\frac{1}{x}dx+c}\] \[=\frac{{{x}^{4}}}{4}\log x-\int{\frac{{{x}^{3}}}{4}dx\,=\,\frac{{{x}^{4}}}{4}\log x-\frac{{{x}^{4}}}{16}+c}\] \[=\frac{1}{16}[4{{x}^{4}}\log x-{{x}^{4}}]+c\].
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