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Beliebt Algebra >

erweitern dulus(e^{-ix}+ie^{ix})^2

Lösung

erweitern

d u l u s (e^{- i x} + i e^{i x})^{2}

Lösung

i (2 l u s cos^{2} (x) d u + 2 l u s sin^{2} (x) d u - 4 l u s cos (x) sin (x) d u)

Schritte zur Lösung

d u l u s (e^{- i x} + i e^{i x})^{2}

(e^{- i x} + i e^{i x})^{2} = - 4 i cos (x) sin (x) + 2 i cos^{2} (x) + 2 i sin^{2} (x)

= l u s d u (2 i cos^{2} (x) + 2 i sin^{2} (x) - 4 i cos (x) sin (x))

= l u s d u (- 4 i cos (x) sin (x) + 2 i cos^{2} (x) + 2 i sin^{2} (x))

Setze Klammern

= d u l u s (- 4 i cos (x) sin (x)) + d u l u s \cdot 2 i cos^{2} (x) + d u l u s \cdot 2 i sin^{2} (x)

Wende Minus-Plus Regeln an

+ (- a) = - a

= - 4 i l u s cos (x) sin (x) d u + 2 i l u s cos^{2} (x) d u + 2 i l u s sin^{2} (x) d u

Schreibe

- 4 i l u s cos (x) sin (x) d u + 2 i l u s cos^{2} (x) d u + 2 i l u s sin^{2} (x) d u

in der Standard komplexen Form um:

(- 4 l u s cos (x) sin (x) d u + 2 l u s cos^{2} (x) d u + 2 l u s sin^{2} (x) d u) i

= (- 4 l u s cos (x) sin (x) d u + 2 l u s cos^{2} (x) d u + 2 l u s sin^{2} (x) d u) i

Beliebte Beispiele

erweitern 12(cos(2x))

e x p an d 12 (cos (2 x))

(d^2)/(dx^2)((y)(5-3x)^3)

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

erweitern (2λ^2)/((λ+s)(2λ+s))

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

erweitern sin(cos((x+y)^2))

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

erweitern (yln(y)-e^{-xy})dx

e x p an d (y ln (y) - e^{- x y}) d x