Google
Câu hỏi: Cho hàm số $f\left( x \right)=\dfrac{1}{3x+1}$. Trong các khẳng định sau, khẳng định nào đúng?
A. $\int{f}(x)\text{d}x=\dfrac{1}{2}\ln \left| 3x+1 \right|+C$.
B. $\int{f}(x)\text{d}x=\dfrac{1}{3}\ln \left| 3x+1 \right|+C$.
C. $\int{f}(x)\text{d}x=\dfrac{1}{3}\ln \left( 3x+1 \right)+C$.
D. $\int{f}(x)\text{d}x=\ln \left| 3x+1 \right|+C$.
A. $\int{f}(x)\text{d}x=\dfrac{1}{2}\ln \left| 3x+1 \right|+C$.
B. $\int{f}(x)\text{d}x=\dfrac{1}{3}\ln \left| 3x+1 \right|+C$.
C. $\int{f}(x)\text{d}x=\dfrac{1}{3}\ln \left( 3x+1 \right)+C$.
D. $\int{f}(x)\text{d}x=\ln \left| 3x+1 \right|+C$.
Theo tính chất: $\int\limits_{{}}^{{}}{f\left( ax+b \right)dx}=\dfrac{1}{a}F\left( ax+b \right)+C$ (với $a\ne 0$ )
Ta có: $\int\limits_{{}}^{{}}{f\left( x \right)dx}=\int\limits_{{}}^{{}}{\dfrac{1}{3x+1}dx}=\dfrac{1}{3}\ln \left| 3x+1 \right|+C$
Ta có: $\int\limits_{{}}^{{}}{f\left( x \right)dx}=\int\limits_{{}}^{{}}{\dfrac{1}{3x+1}dx}=\dfrac{1}{3}\ln \left| 3x+1 \right|+C$
Đáp án B.