integral of e^{ax}x

Lösung

\int e^{a x} x d x

e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}} + C

Schritte zur Lösung

\int e^{a x} x d x

Wende die partielle Integration an

= e^{a x} \frac{1}{a} x - \int e^{a x} \frac{1}{a} d x

\int e^{a x} \frac{1}{a} d x = e^{a x} \frac{1}{a ^{2}}

= e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}}

Füge eine Konstante zur Lösung hinzu

= e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}} + C

\frac{d}{d x} (5 g (x) (2 x^{3}) + \frac{2}{x ^{2}})

\int_{0}^{3} e^{- 2 x} d x

\frac{\partial}{\partial x} (2 x y e^{- x^{2} y})

\int \frac{x + 5}{4 - ( x - 2 ) ^{2}} d x

\int sin^{2} (9 x) cos^{2} (9 x) d x