erweitern ((1/2 (e^{x^2}x^2-e^{x^2})+C))/(e^{x^2)}

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

Füge

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

zusammen:

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

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

Wende Bruchregel an:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Teile die Zahlen:

\frac{2}{2} = 1

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

Streiche

\frac{x ^{2} e ^{x^{2}}}{2 e ^{x^{2}}} : \frac{x ^{2}}{2}

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

Streiche

\frac{e ^{x^{2}}}{2 e ^{x^{2}}} : \frac{1}{2}

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

e x p an d \frac{e ^{s} + 2 s + 2}{s ( s + 1 ) ^{2}}

e x p an d x (1, 50 + 3 + 4.5 + 3)

e x p an d \frac{n}{2 ( n + 1 )}

e x p an d (y x + y^{2} + y) d x + (x + 2 y) d y

e x p an d \frac{b ^{3} - c ^{3} - 3 c b ^{2} + 3 c ^{2} b}{( b - c ) ( b ^{2} - c ^{2} )}