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Beliebt Rechnen >

integral of (t+1)^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

= \int t^{2} + 2 t + 1 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 t^{2} d t + \int 2 t d t + \int 1 d t

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

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

\int 1 d t = t

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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