integral of (3-x)/2

Lösung

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

\frac{1}{2} (3 x - \frac{x ^{2}}{2}) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 3 - 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

= \frac{1}{2} (\int 3 d x - \int x d x)

\int 3 d x = 3 x

\int x d x = \frac{x ^{2}}{2}

= \frac{1}{2} (3 x - \frac{x ^{2}}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (3 x - \frac{x ^{2}}{2}) + C

\int \frac{2 x - 1}{( x - 2 ) ( x - 3 ) ( x + 1 )} d x

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