integral of x^4e^{5x}

Lösung

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

\frac{1}{5} e^{5 x} x^{4} - \frac{4}{3125} (125 e^{5 x} x^{3} - 3 (25 e^{5 x} x^{2} - 2 (5 e^{5 x} x - e^{5 x}))) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{5} e^{5 x} x^{4} - \int \frac{4}{5} e^{5 x} x^{3} d x

\int \frac{4}{5} e^{5 x} x^{3} d x = \frac{4}{3125} (125 e^{5 x} x^{3} - 3 (25 e^{5 x} x^{2} - 2 (5 e^{5 x} x - e^{5 x})))

= \frac{1}{5} e^{5 x} x^{4} - \frac{4}{3125} (125 e^{5 x} x^{3} - 3 (25 e^{5 x} x^{2} - 2 (5 e^{5 x} x - e^{5 x})))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} e^{5 x} x^{4} - \frac{4}{3125} (125 e^{5 x} x^{3} - 3 (25 e^{5 x} x^{2} - 2 (5 e^{5 x} x - e^{5 x}))) + C

f (x) = \frac{3}{x + 5}

d er i v a t i v e y = \frac{3}{x ^{6}} + \frac{1}{x ^{5}} - \frac{7}{x ^{2}}

\frac{\partial}{\partial x} (x \cdot sin (4 \cdot y \cdot z^{4}))

t an g e n t f (x) = 2 x^{2} - 4 x, at x = - 1

t an g e n t f (x) = 4 x - x^{2}, (2, 5)