integral of xe^{ix}

Lösung

\int x e^{i x} d x

x sin (x) + cos (x) + i (sin (x) - x cos (x)) + C

Schritte zur Lösung

\int x e^{i x} d x

Vereinfache

x e^{i x} : x cos (x) + i x sin (x)

= \int x cos (x) + i x sin (x) 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 x cos (x) d x + \int i x sin (x) d x

\int x cos (x) d x = x sin (x) + cos (x)

\int i x sin (x) d x = i (sin (x) - x cos (x))

= x sin (x) + cos (x) + i (sin (x) - x cos (x))

Füge eine Konstante zur Lösung hinzu

= x sin (x) + cos (x) + i (sin (x) - x cos (x)) + C

\int 8 sin (x) d x

a re a y = \frac{5}{x}, y = \frac{3}{x}, x = 1, x = 5

\int (x^{4} + 2 x^{3} - 5 x + 9) d x

x \to o lim (e^{x})

\int \frac{x ^{4}}{( 1 - x ) ^{3}} d x