A) \[x+\frac{16}{x}+\frac{64}{3{{x}^{2}}}+c\]
B) \[x-\frac{16}{x}-\frac{64}{3{{x}^{3}}}+c\]
C) \[x-\frac{32}{{{x}^{3}}}-\frac{256}{3{{x}^{2}}}+c\]
D) None of these
Correct Answer: B
Solution :
\[\int{\frac{{{({{x}^{2}}+x)}^{2}}}{{{x}^{4}}}}dx=\int{\left( \frac{{{x}^{4}}+64+16{{x}^{2}}}{{{x}^{4}}} \right)}dx\] \[=\int{\left( 1+\frac{64}{{{x}^{4}}}+\frac{16}{{{x}^{2}}} \right)}dx\] \[=\left[ x-\frac{64}{3{{x}^{3}}}-\frac{16}{x}+c \right]\] \[=x-\frac{16}{x}-\frac{64}{3{{x}^{3}}}+c\]
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