A) \[5({{x}^{7}}+x){{\tan }^{-1}}x+c\]
B) \[{{x}^{5}}-\frac{5}{3}{{x}^{3}}+5x+c\]
C) \[3{{x}^{4}}-5{{x}^{2}}+15x+c\]
D) \[5{{\tan }^{-1}}({{x}^{2}}+1)+\log ({{x}^{2}}+1)+c\]
Correct Answer: B
Solution :
\[\int_{{}}^{{}}{\frac{5({{x}^{6}}+1)}{{{x}^{2}}+1}\,dx=\int_{{}}^{{}}{\frac{5({{x}^{2}}+1)({{x}^{4}}-{{x}^{2}}+1)}{({{x}^{2}}+1)}\,dx}}\] \[=\int_{{}}^{{}}{5({{x}^{4}}-{{x}^{2}}+1)\,dx={{x}^{5}}-\frac{5}{3}{{x}^{3}}+5x+c.}\]
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