A. \(\int{\frac{2}{4x-3}\,\text{d}x}=2\ln \left( 2x-\frac{3}{2} \right)+C.\)
B. \(\int{\frac{2}{4x-3}\,\text{d}x}=\frac{1}{4}\ln \left| 4x-3 \right|+C.\)
C. \(\int{\frac{2}{4x-3}\,\text{d}x}=\frac{1}{2}\ln \left| 2x-\frac{3}{2} \right|+C.\)
D. \(\int{\frac{2}{4x-3}\,\text{d}x}=\frac{1}{2}\ln \left( 2x-\frac{3}{2} \right)+C.\)
C
Ta có \(\int{f\left( x \right)\,\text{d}x}=\int{\frac{2}{4x-3}\,\text{d}x}=\frac{2}{4}\ln \left| 4x-3 \right|+C=\frac{1}{2}\ln \left| 2\left( 2x-\frac{3}{2} \right) \right|+C=\frac{1}{2}\ln \left| 2x-\frac{3}{2} \right|+C.\)
Chọn C
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