Cho \( \int {f(x)dx} = F(x) + C\) . Khi đó \( \int {f(2x – 3)dx} \)

Đặt \(\begin{array}{l}
t = 2x – 3 \Rightarrow dt = 2xdx\\
\smallint f\left( {2x – 3} \right)dx = \frac{1}{2}\smallint f\left( t \right)dt
\end{array}\)

Mà 

\(
\smallint f\left( x \right)dx = F\left( x \right) + C \to \smallint f\left( t \right)dt = F\left( t \right) + C = F\left( {2x – 3} \right) + C\)

Vậy: \(
\smallint f\left( {2x – 3} \right)dx = \frac{1}{2}F\left( {2x – 3} \right) + C\)