integral of (sin(x))/(x^2+1)

Lösung

\int \frac{sin ( x )}{x ^{2} + 1} d x

\frac{1}{4 e} ((e^{2} - 1) Ci (i - x) + (e^{2} - 1) Ci (x + i) + i (1 + e^{2}) (Si (i - x) + Si (x + i))) + C

Schritte zur Lösung

\int \frac{sin ( x )}{x ^{2} + 1} d x

Das ist ein nicht elementares Integral :

\int \frac{sin ( x )}{x ^{2} + 1} d x = \frac{1}{4 e} ((e^{2} - 1) Ci (i - x) + (e^{2} - 1) Ci (x + i) + i (1 + e^{2}) (Si (i - x) + Si (x + i)))

= \frac{1}{4 e} ((e^{2} - 1) Ci (i - x) + (e^{2} - 1) Ci (x + i) + i (1 + e^{2}) (Si (i - x) + Si (x + i)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4 e} ((e^{2} - 1) Ci (i - x) + (e^{2} - 1) Ci (x + i) + i (1 + e^{2}) (Si (i - x) + Si (x + i))) + C

l a pl a ce t r an s f or m 2 e^{- 3 t}

\int 17 x^{2} sin (π x) d x

\int - x + 1 d x

x \to 1 lim (a x^{2} + b x + 1)

d er i v a t i v e f (x) = - 2 t^{2} + 3 t - 6