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Câu hỏi: $\int\left(3^x-\dfrac{1}{3^x}\right)^2 \mathrm{~d} x$ bằng
A. $\dfrac{1}{3}\left(\dfrac{3^x}{\ln 3}-\dfrac{1}{3^x \ln 3}\right)^3+C$.
B. $\dfrac{9^x}{2 \ln 3}-\dfrac{1}{2 \cdot 9^x \cdot \ln 3}-2 x+C$.
C. $\dfrac{1}{2 \ln 3}\left(9^x+\dfrac{1}{9^x}\right)-2 x+C$.
D. $\left(\dfrac{3^x}{\ln 3}-\dfrac{\ln 3}{3^x}\right)^2+C$.
A. $\dfrac{1}{3}\left(\dfrac{3^x}{\ln 3}-\dfrac{1}{3^x \ln 3}\right)^3+C$.
B. $\dfrac{9^x}{2 \ln 3}-\dfrac{1}{2 \cdot 9^x \cdot \ln 3}-2 x+C$.
C. $\dfrac{1}{2 \ln 3}\left(9^x+\dfrac{1}{9^x}\right)-2 x+C$.
D. $\left(\dfrac{3^x}{\ln 3}-\dfrac{\ln 3}{3^x}\right)^2+C$.
$
\begin{aligned}
& \int\left(3^x-\dfrac{1}{3^x}\right)^2 \mathrm{~d} x=\int\left(3^{2 x}+\dfrac{1}{3^{2 x}}-2\right) \mathrm{d} x=\int 3^{2 x} \mathrm{~d} x+\int 3^{-2 x} \mathrm{~d} x-2 \int \mathrm{d} x=\dfrac{1}{2} \cdot \dfrac{3^{2 x}}{\ln 3}-\dfrac{1}{2} \cdot \dfrac{1}{3^{2 x} \ln 3}- \\
& 2 x+C \\
& =\dfrac{1}{2} \cdot \dfrac{9^x}{\ln 3}-\dfrac{1}{2} \cdot \dfrac{1}{9^x \ln 3}-2 x+C .
\end{aligned}
$
\begin{aligned}
& \int\left(3^x-\dfrac{1}{3^x}\right)^2 \mathrm{~d} x=\int\left(3^{2 x}+\dfrac{1}{3^{2 x}}-2\right) \mathrm{d} x=\int 3^{2 x} \mathrm{~d} x+\int 3^{-2 x} \mathrm{~d} x-2 \int \mathrm{d} x=\dfrac{1}{2} \cdot \dfrac{3^{2 x}}{\ln 3}-\dfrac{1}{2} \cdot \dfrac{1}{3^{2 x} \ln 3}- \\
& 2 x+C \\
& =\dfrac{1}{2} \cdot \dfrac{9^x}{\ln 3}-\dfrac{1}{2} \cdot \dfrac{1}{9^x \ln 3}-2 x+C .
\end{aligned}
$
Đáp án B.