Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
f\left( x \right) = \int {f'\left( x \right)} \\
\Leftrightarrow f\left( x \right) = \int {\frac{1}{{2x - 1}}dx} \\
\Leftrightarrow f\left( x \right) = \int {\frac{{\frac{{d\left( {2x - 1} \right)}}{2}}}{{2x - 1}}} \\
\Rightarrow f\left( x \right) = \frac{1}{2}\ln \left| {2x - 1} \right| + C\\
\Rightarrow \left[ \begin{array}{l}
f\left( x \right) = \frac{1}{2}\ln \left( {2x - 1} \right) + {C_1},\,\,\,\,\,\,\left( {x > \frac{1}{2}} \right)\\
f\left( x \right) = \frac{1}{2}\ln \left( {1 - 2x} \right) + {C_2},\,\,\,\,\,\,\left( {x < \frac{1}{2}} \right)
\end{array} \right.\\
f\left( 0 \right) = 1 \Leftrightarrow \frac{1}{2}\ln \left( {1 - 2.0} \right) + {C_2} = 1 \Leftrightarrow {C_2} = 1\\
f\left( 1 \right) = 2 \Leftrightarrow \frac{1}{2}\ln \left( {2.1 - 1} \right) + {C_1} = 2 \Leftrightarrow {C_1} = 2
\end{array}\)
