integral of x^45^x

Lösung

\int x^{4} 5^{x} d x

\frac{5 ^{x} x ^{4}}{ln ( 5 )} - \frac{4}{ln ( 5 )} (\frac{5 ^{x} x ^{3}}{ln ( 5 )} - \frac{3}{ln ( 5 )} (\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )}))) + C

Schritte zur Lösung

\int x^{4} \cdot 5^{x} d x

Wende die partielle Integration an

= \frac{5 ^{x} x ^{4}}{ln ( 5 )} - \int \frac{4 \cdot 5 ^{x} x ^{3}}{ln ( 5 )} d x

\int \frac{4 \cdot 5 ^{x} x ^{3}}{ln ( 5 )} d x = \frac{4}{ln ( 5 )} (\frac{5 ^{x} x ^{3}}{ln ( 5 )} - \frac{3}{ln ( 5 )} (\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )})))

= \frac{5 ^{x} x ^{4}}{ln ( 5 )} - \frac{4}{ln ( 5 )} (\frac{5 ^{x} x ^{3}}{ln ( 5 )} - \frac{3}{ln ( 5 )} (\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )})))

Füge eine Konstante zur Lösung hinzu

= \frac{5 ^{x} x ^{4}}{ln ( 5 )} - \frac{4}{ln ( 5 )} (\frac{5 ^{x} x ^{3}}{ln ( 5 )} - \frac{3}{ln ( 5 )} (\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )}))) + C

t an g e n t f (x) = (x^{2} - 48)^{4}, at x = 7

\frac{d}{d x} (\frac{x}{3 x + 4 ln ( x )})

\frac{d}{d x} (x + 11)

\int_{0}^{\frac{3}{2}} x cos (π) x d x

d er i v a t i v e 2 (2 e^{x^{2}} x^{2} + e^{x^{2}})