Google
Câu hỏi: Họ nguyên hàm của hàm số $f\left( x \right)={{2}^{x}}+\text{cos}2x$ là
A. ${{2}^{x}}+\text{sin}2x+C$.
B. ${{2}^{x}}\ln 2-2\text{sin}2x+C$.
C. $\dfrac{{{2}^{x}}}{\ln 2}-\text{sin}2x+C$.
D. $\dfrac{{{2}^{x}}}{\ln 2}\text{+}\dfrac{\text{sin}2x}{2}+C$.
A. ${{2}^{x}}+\text{sin}2x+C$.
B. ${{2}^{x}}\ln 2-2\text{sin}2x+C$.
C. $\dfrac{{{2}^{x}}}{\ln 2}-\text{sin}2x+C$.
D. $\dfrac{{{2}^{x}}}{\ln 2}\text{+}\dfrac{\text{sin}2x}{2}+C$.
$\int{f\left( x \right)}\text{d}x=\int{\left( {{2}^{x}}+\text{cos}2x \right)}\text{d}x=\int{{{2}^{x}}}\text{d}x+\int{\text{cos}2x}\text{d}x=\dfrac{{{2}^{x}}}{\ln 2}+\dfrac{\text{sin}2x}{2}+C.$
Đáp án D.