integral of x^2e^{5x}

Lösung

\int x^{2} e^{5 x} d x

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

Schritte zur Lösung

\int x^{2} e^{5 x} d x

Wende die partielle Integration an

= \frac{1}{5} e^{5 x} x^{2} - \int \frac{2}{5} e^{5 x} x d x

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

= \frac{1}{5} e^{5 x} x^{2} - \frac{2}{125} (5 e^{5 x} x - e^{5 x})

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e 8 e^{- x} + e^{3 x}

\int - 2 tan (t) d t

\int tan^{5} (θ) sec^{3} (θ) d θ

\frac{\partial}{\partial x} (x^{3} z + z^{3} x - 2 yz)

t an g e n t f (x) = x^{2} x^{3} + 1, at x = 1