integral of x(e^x+e^{x^2})

Lösung

\int x (e^{x} + e^{x^{2}}) d x

e^{x} x - e^{x} + \frac{1}{2} e^{x^{2}} + C

Schritte zur Lösung

\int x (e^{x} + e^{x^{2}}) d x

Multipliziere aus

x (e^{x} + e^{x^{2}}) : e^{x} x + e^{x^{2}} x

= \int e^{x} x + e^{x^{2}} x d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{x} x d x + \int e^{x^{2}} x d x

\int e^{x} x d x = e^{x} x - e^{x}

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

= e^{x} x - e^{x} + \frac{1}{2} e^{x^{2}}

Füge eine Konstante zur Lösung hinzu

= e^{x} x - e^{x} + \frac{1}{2} e^{x^{2}} + C

a re a 2 x^{2} + 11, 0, - 2, 2

t an g e n t f (x) = x^{3} - 2 x + 2, at x = 4

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

\frac{d}{d x} (1 - e^{- \frac{x}{2}})

s l o p e \frac{1}{x - 5}