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Câu hỏi: Tìm nguyên hàm của hàm số $f(x)=\dfrac{2\text{x}+1}{2\text{x}-3}$.
A. $\int{f(x)d\text{x}}=x+\ln \left| 2x-3 \right|+C$
B. $\int{f(x)d\text{x}}=x+\dfrac{1}{2}\ln \left| 2\text{x}-3 \right|+C$
C. $\int{f(x)d\text{x}}=x+2\ln \left| 2\text{x}-3 \right|+C$
D. $\int{f(x)dx}=2\text{x}+2\ln \left| 2\text{x}-3 \right|+C$
A. $\int{f(x)d\text{x}}=x+\ln \left| 2x-3 \right|+C$
B. $\int{f(x)d\text{x}}=x+\dfrac{1}{2}\ln \left| 2\text{x}-3 \right|+C$
C. $\int{f(x)d\text{x}}=x+2\ln \left| 2\text{x}-3 \right|+C$
D. $\int{f(x)dx}=2\text{x}+2\ln \left| 2\text{x}-3 \right|+C$
Ta có $\int{f(x)d\text{x}}=\int{\dfrac{2\text{x}+1}{2\text{x}-3}d\text{x}}=\int{\left( 1+\dfrac{4}{2\text{x}-3} \right)d\text{x}}=x+2\ln \left| 2\text{x}-3 \right|+C$.
Đáp án C.