A) \[a\log x+\frac{b}{{{x}^{3}}}+\frac{c}{3{{x}^{3}}}+A\]
B) \[a\log x+\frac{b}{x}-\frac{c}{3{{x}^{3}}}+A\]
C) \[a\log x-\frac{b}{x}-\frac{c}{3{{x}^{3}}}+A\]
D) \[a\log x+\frac{b}{x}+\frac{c}{3{{x}^{3}}}+A\]
Correct Answer: C
Solution :
\[\int{\left( \frac{a{{x}^{3}}+b{{x}^{2}}+c}{{{x}^{4}}} \right)}dx\] \[=\int{\left( \frac{a}{x}+\frac{b}{{{x}^{2}}}+\frac{c}{{{x}^{4}}} \right)}dx\] \[=a\log x-\frac{b}{x}-\frac{x}{3{{x}^{3}}}+A\]
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