Voorbeeld 1.
$
\eqalign{
& \int {e^{2x + 1} } dx \cr
& Kies\,\,t = 2x + 1 \to \frac{{dt}}
{{dx}} = 2 \Rightarrow dt = 2dx \cr
& \int {e^{2x + 1} \,dx = \int {\frac{1}
{2}e^{2x + 1} \cdot 2dx = \int {\frac{1}
{2}e^t \,dt = \frac{1}
{2}e^t = \frac{1}
{2}e^{2x + 1} } } } \cr}
$
Voorbeeld 2.
$
\eqalign{
& \int {xe^{x^2 } } dx \cr
& Kies\,\,t = x^2 \to \frac{{dt}}
{{dx}} = 2x \Rightarrow dt = 2x\,dx \cr
& \int {xe^{x^2 } dx = \int {\frac{1}
{2}e^{x^2 } \cdot 2x\,dx = \int {\frac{1}
{2}e^t \,dt = \frac{1}
{2}e^t = \frac{1}
{2}e^{x^2 } } } } \cr}
$
Voorbeeld 3.
$
\eqalign{
& \int {\frac{{e^x }}
{{1 + e^{2x} }}dx} \cr
& Kies\,\,t = e^x \to \frac{{dt}}
{{dx}} = e^x \Rightarrow dt = e^x \,dx \cr
& \int {\frac{{e^x }}
{{1 + e^{2x} }}dx} = \int {\frac{1}
{{1 + e^{2x} }} \cdot e^x dx} = \int {\frac{1}
{{1 + t^2 }}} \,dt = \arctan (t) = \arctan (e^x ) \cr}
$
