A) \[\frac{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{12}}}{12}+c\]
B) \[\frac{{{(4{{x}^{3}}+9{{x}^{2}}+18x+8)}^{13}}}{13}+c\]
C) \[\frac{{{({{x}^{4}}+3{{x}^{2}}+9{{x}^{2}}+8x-6)}^{13}}}{13}+c\]
D) \[\frac{{{({{x}^{4}}+3{{x}^{2}}+9{{x}^{2}}+8x-6)}^{11}}}{11}+c\]
Correct Answer: C
Solution :
\[\int{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{12}}}\] \[(4{{x}^{3}}+9{{x}^{2}}+18x+8)dx\] \[=\frac{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{13}}}{13}+C\] \[\left[ \because \,\,\int{{{\{f(x)\}}^{n}}\,f'(x)\,dx=\frac{{{\{f(x)\}}^{n+1}}}{n+1}} \right]\]
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