integral of e^{x^2-4}+5x+6

Lösung

\int e^{x^{2} - 4} + 5 x + 6 d x

\frac{π}{2 e ^{4}} erfi (x) + \frac{5 x ^{2}}{2} + 6 x + C

Schritte zur Lösung

\int e^{x^{2} - 4} + 5 x + 6 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^{2} - 4} d x + \int 5 x d x + \int 6 d x

\int e^{x^{2} - 4} d x = \frac{π}{2 e ^{4}} erfi (x)

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= \frac{π}{2 e ^{4}} erfi (x) + \frac{5 x ^{2}}{2} + 6 x

Füge eine Konstante zur Lösung hinzu

= \frac{π}{2 e ^{4}} erfi (x) + \frac{5 x ^{2}}{2} + 6 x + C

d er i v a t i v e y = \frac{x}{2 + x}

x \to - 2 - lim (- x - 2 + 4)

t \to 2 lim ([e^{- 3 t} i])

\int_{- 5}^{- 7} (- 5)^{- 3} d x

\frac{d}{d x} (\frac{2}{5} x^{5} - 3 x^{2} + 8 x - 5)