integral of xa^x

Lösung

\int x a^{x} d x

\frac{a ^{x} x}{ln ( a )} - \frac{a ^{x}}{ln ^{2} ( a )} + C

Schritte zur Lösung

\int x a^{x} d x

Wende die partielle Integration an

= \frac{a ^{x} x}{ln ( a )} - \int \frac{a ^{x}}{ln ( a )} d x

\int \frac{a ^{x}}{ln ( a )} d x = \frac{a ^{x}}{ln ^{2} ( a )}

= \frac{a ^{x} x}{ln ( a )} - \frac{a ^{x}}{ln ^{2} ( a )}

Füge eine Konstante zur Lösung hinzu

= \frac{a ^{x} x}{ln ( a )} - \frac{a ^{x}}{ln ^{2} ( a )} + C

\int \frac{x ^{2}}{( 196 + x ^{2} ) ^{2}} d x

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

\int \frac{x ^{2} - 1}{x ^{3}} d x

\frac{d y}{d t} = 6 e^{2 t - y}

\frac{d}{d x} (m x e^{n x^{2}})