integral of (sin(x)-x)/x

Lösung

\int \frac{sin ( x ) - x}{x} d x

Si (x) - x + C

Schritte zur Lösung

\int \frac{sin ( x ) - x}{x} d x

Multipliziere aus

\frac{sin ( x ) - x}{x} : \frac{sin ( x )}{x} - 1

= \int \frac{sin ( x )}{x} - 1 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 \frac{sin ( x )}{x} d x - \int 1 d x

\int \frac{sin ( x )}{x} d x = Si (x)

\int 1 d x = x

= Si (x) - x

Füge eine Konstante zur Lösung hinzu

= Si (x) - x + C

\int \frac{1 - x ^{2} - 3 x ^{2}}{x ^{\frac{2}{3}}} d x

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

\int (sec^{2} (x) (1 + tan (x))) d x

\int - e^{- x} sin (e^{- x}) d x

\int x^{\frac{1}{3}} e^{x^{\frac{1}{3}}} d x