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Beliebt Rechnen >

integral of (1-t)(2+t^2)

Lösung

\int (1 - t) (2 + t^{2}) d t

Lösung

2 t + \frac{t ^{3}}{3} - t^{2} - \frac{t ^{4}}{4} + C

Schritte zur Lösung

\int (1 - t) (2 + t^{2}) d t

Multipliziere aus

(1 - t) (2 + t^{2}) : 2 + t^{2} - 2 t - t^{3}

= \int 2 + t^{2} - 2 t - t^{3} d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 d t + \int t^{2} d t - \int 2 t d t - \int t^{3} d t

\int 2 d t = 2 t

\int t^{2} d t = \frac{t ^{3}}{3}

\int 2 t d t = t^{2}

\int t^{3} d t = \frac{t ^{4}}{4}

= 2 t + \frac{t ^{3}}{3} - t^{2} - \frac{t ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= 2 t + \frac{t ^{3}}{3} - t^{2} - \frac{t ^{4}}{4} + C

Graph

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