A) \[2a{{x}^{2}}+3b{{x}^{3}}+4c{{x}^{4}}+k\]
B) \[6a{{x}^{2}}+4b{{x}^{3}}+3c{{x}^{4}}+k\]
C) \[a+b+c{{x}^{2}}+k\]
D) \[\frac{1}{2}a{{x}^{2}}+\frac{1}{3}b{{x}^{3}}+\frac{1}{4}c{{x}^{4}}+k\]
Correct Answer: D
Solution :
\[\int_{{}}^{{}}{\frac{a{{x}^{-2}}+b{{x}^{-1}}+c}{{{x}^{-3}}}\,dx}=\int_{{}}^{{}}{(ax+b{{x}^{2}}+c{{x}^{3}})\,dx}\] \[=\frac{1}{4}c{{x}^{4}}+\frac{1}{3}b{{x}^{3}}+\frac{1}{2}a{{x}^{2}}+k.\]
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