Intégration par parties de puissances de fonction

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se souvenir que f'(x) * f(x)^k est immédiat
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Question Answer
\[\int f'(x) f(x)^k dx \] \[\frac{f(x)^{k+1}}{k+1} + C\]
\[\int cos(x) sin² (x) dx \] \[\frac{sin³(x)}{3} + C\]
\[\int sin(x) cos² (x) dx \] \[- \frac{cos³(x)}{3} + C\]
\[\int a e^{ax} dx \] \[ e^{ax} + C\]
\[\int \frac{[ln(x)]^a}{x} dx \] \[ \frac {[ln(x)]^{a+1}}{a+1} + C\]
\[\int \frac{tg^2(x)}{cos^2(x)} dx \] \[ \frac {tg^3(x)}{3} + C\]
\[\int f'(x) f(x) e^{\frac {f^2(x)}{2}} dx \] \[ e^{\frac {f^2(x)}{2}} + C \]
\[\int cos(x) e^{sin(x)}dx \] \[ e^{sin(x)} + C \]
\[\int x e^{\frac {x^2}{2}} dx \] \[\int x e^{\frac {x^2}{2}} dx \]
\[\int \frac{tg^2(x)}{cos^2(x)} e^{\frac {tg^3(x)}{3}} dx \] \[ e^{\frac {tg^3(x)}{3}} + C \]
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