A) \[a\log x+\frac{b}{{{x}^{2}}}+\frac{c}{3{{x}^{3}}}+c\]
B) \[a\log x+\frac{b}{x}-\frac{c}{3{{x}^{3}}}+c\]
C) \[a\log x-\frac{b}{x}-\frac{c}{3{{x}^{3}}}+c\]
D) None of these
Correct Answer: C
Solution :
\[I=\int{\frac{a{{x}^{3}}+b{{x}^{2}}+c}{{{x}^{4}}}dx=\int{\left[ \frac{a}{x}+\frac{b}{{{x}^{2}}}+\frac{c}{{{x}^{4}}} \right]\,dx}}\] \[=a\log x-\frac{b}{x}-\frac{c}{3{{x}^{3}}}+c\].
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