Voorbeeld 1
$
\int {\sin ^3 x\,\,dx = } \int {\sin ^2 x\sin x\,\,dx} = \int {\left( {1 - \cos ^2 x} \right)d( - \cos x)}
$
Kies $
u = -\cos (x)
$
$
\int {1 - u^2 \,du = u - \frac{1}{3}u^3 + C = - \cos x + \frac{1}{3}\cos ^3 x + C}
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Voorbeeld 2
$
\begin{array}{l}
\int{\cos ^5 x} \,dx =\int{\cos ^4 x \cos x} \,dx =\int{\left( {1 - \sin ^2 x} \right)^2 } d\left( {\sin x} \right) = \\
\int {\left( {1 - u^2 } \right)^2 du} = \int {\left( {1 - 2u^2 + u^4 } \right)du} = \\
u - \frac{2}{3}u^3 + \frac{1}{5}u^5 = \sin x - \frac{2}{3}\sin ^3 x + \frac{1}{5}\sin ^5 x \\
\end{array}
$