erweitern (te^t+te^{2t})^2

Lösung

erweitern

(t e^{t} + t e^{2 t})^{2}

e^{2 t} t^{2} + 2 e^{3 t} t^{2} + e^{4 t} t^{2}

Schritte zur Lösung

(t e^{t} + t e^{2 t})^{2}

= (e^{t} t + e^{2 t} t)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = t e^{t}, b = t e^{2 t}

= (t e^{t})^{2} + 2 t e^{t} t e^{2 t} + (t e^{2 t})^{2}

Vereinfache

(t e^{t})^{2} + 2 t e^{t} t e^{2 t} + (t e^{2 t})^{2} : e^{2 t} t^{2} + 2 e^{3 t} t^{2} + e^{4 t} t^{2}

= e^{2 t} t^{2} + 2 e^{3 t} t^{2} + e^{4 t} t^{2}

e x p an d - \frac{40 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

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

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

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

e x p an d \frac{x ( 2 x ^{3} + y )}{6 y ^{2}}