integral of 1+e^{x^2}

Lösung

\int 1 + e^{x^{2}} d x

x + \frac{π}{2} erfi (x) + C

Schritte zur Lösung

\int 1 + e^{x^{2}} 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 1 d x + \int e^{x^{2}} d x

\int 1 d x = x

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

= x + \frac{π}{2} erfi (x)

Füge eine Konstante zur Lösung hinzu

= x + \frac{π}{2} erfi (x) + C

\frac{\partial}{\partial y} (e^{x^{2} + y^{2}} \cdot 2 y)

\int \frac{x ^{\frac{1}{3}} - 3}{x ^{\frac{2}{3}}} d x

\int_{0}^{2} 1 + 4 x^{2} d x

q^{^{'}} + \frac{q}{20 + t} = 1, q (0) = 5

d er i v a t i v e x^{8} (x - 3)^{7}