integral from 0 to 1 of x^4e^{6x}

Lösung

\int_{0}^{1} x^{4} e^{6 x} d x

\frac{31 e ^{6} - 1}{324}

Dezimale

38.59658 \dots

Schritte zur Lösung

\int_{0}^{1} x^{4} e^{6 x} d x

Wende die partielle Integration an

= [\frac{1}{6} e^{6 x} x^{4} - \int \frac{2}{3} e^{6 x} x^{3} d x]_{0}^{1}

\int \frac{2}{3} e^{6 x} x^{3} d x = \frac{1}{324} e^{6 x} (36 x^{3} - 18 x^{2} + 6 x - 1)

= [\frac{1}{6} e^{6 x} x^{4} - \frac{1}{324} e^{6 x} (36 x^{3} - 18 x^{2} + 6 x - 1)]_{0}^{1}

Berechne die Grenzen:

\frac{31 e ^{6}}{324} - \frac{1}{324}

= \frac{31 e ^{6}}{324} - \frac{1}{324}

Vereinfache

= \frac{31 e ^{6} - 1}{324}

\int - t z d t

e^{2 x} y^{^{'}} - 2 e^{2 x} y = 3 e^{4 x}

x \to 5 - lim (\frac{12}{5 - x})

\frac{d}{d x} (e^{x} (8 x^{2} - 16 x + 16))

\int x^{- 6} d x