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Câu hỏi: Tìm họ nguyên hàm của hàm số $y={{x}^{2}}-{{3}^{x}}+\dfrac{2}{x}$.
A. $\dfrac{{{x}^{3}}}{3}-\dfrac{{{3}^{x}}}{\ln 3}-\dfrac{2}{{{x}^{2}}}+C,\text{ C}\in \mathbb{R}$
B. $\dfrac{{{x}^{3}}}{3}-{{3}^{x}}+\dfrac{2}{{{x}^{2}}}+C,\text{ C}\in \mathbb{R}$
C. $\dfrac{{{x}^{3}}}{3}-\dfrac{{{3}^{x}}}{\ln 3}+2\ln \left| x \right|+C,\text{ C}\in \mathbb{R}$
D. $\dfrac{{{x}^{3}}}{3}-\dfrac{{{3}^{x}}}{\ln 3}-2\ln \left| x \right|+C,\text{ C}\in \mathbb{R}$
A. $\dfrac{{{x}^{3}}}{3}-\dfrac{{{3}^{x}}}{\ln 3}-\dfrac{2}{{{x}^{2}}}+C,\text{ C}\in \mathbb{R}$
B. $\dfrac{{{x}^{3}}}{3}-{{3}^{x}}+\dfrac{2}{{{x}^{2}}}+C,\text{ C}\in \mathbb{R}$
C. $\dfrac{{{x}^{3}}}{3}-\dfrac{{{3}^{x}}}{\ln 3}+2\ln \left| x \right|+C,\text{ C}\in \mathbb{R}$
D. $\dfrac{{{x}^{3}}}{3}-\dfrac{{{3}^{x}}}{\ln 3}-2\ln \left| x \right|+C,\text{ C}\in \mathbb{R}$
Ta có: $\int{\left( {{x}^{2}}-{{3}^{x}}+\dfrac{1}{x} \right)d\text{x}}=\dfrac{{{x}^{3}}}{3}-\dfrac{{{3}^{x}}}{\ln 3}+2\ln \left| x \right|+C,C\in \mathbb{R}$.
Đáp án C.