erweitern (xcos(x)+sin(x))^2

Lösung

erweitern

(x cos (x) + sin (x))^{2}

x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

Schritte zur Lösung

(x cos (x) + sin (x))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(x cos (x) + sin (x))^{2} = (x cos (x))^{2} + 2 x cos (x) sin (x) + sin^{2} (x)

= (x cos (x))^{2} + 2 x cos (x) sin (x) + sin^{2} (x)

Vereinfache

(x cos (x))^{2} + 2 x cos (x) sin (x) + sin^{2} (x) : x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

= x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

e x p an d \frac{4 e ^{- 3 t}}{( s - 3 ) ( s + 1 )}

s im pl i f y (2 x + \frac{1}{x ^{2}}) (5 - x) (2 x^{5} + 1)^{3}

e x p an d \frac{2 ( - 4 x - 12 )}{x ^{2} - 12 x + 36}

e x p an d \frac{3 ( 15 + 7 5 )}{4}

e x p an d \frac{2 ( 7 \cdot 7 ^{\frac{1}{2}} - 3 \cdot 3 ^{\frac{1}{2}} )}{9 \cdot 3 ^{\frac{1}{2}}}