integral of x^2e^{20x}

Lösung

\int x^{2} e^{20 x} d x

\frac{1}{20} e^{20 x} x^{2} - \frac{1}{4000} (20 e^{20 x} x - e^{20 x}) + C

Schritte zur Lösung

\int x^{2} e^{20 x} d x

Wende die partielle Integration an

= \frac{1}{20} e^{20 x} x^{2} - \int \frac{1}{10} e^{20 x} x d x

\int \frac{1}{10} e^{20 x} x d x = \frac{1}{4000} (20 e^{20 x} x - e^{20 x})

= \frac{1}{20} e^{20 x} x^{2} - \frac{1}{4000} (20 e^{20 x} x - e^{20 x})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{20} e^{20 x} x^{2} - \frac{1}{4000} (20 e^{20 x} x - e^{20 x}) + C

d er i v a t i v e f (x) = 2 π x

t an g e n t f (x) = x + 7, at x = 2

\frac{d}{d x} (\frac{7 x - 11}{x})

y^{^{'}} = 9 x e^{y}, y (0) = 0

\int \frac{1}{x ^{3} x ^{2} - 9} d x