integral of (t+200)^2

Lösung

\int (t + 200)^{2} d t

\frac{t ^{3}}{3} + 200 t^{2} + 40000 t + C

Schritte zur Lösung

\int (t + 200)^{2} d t

Multipliziere aus

(t + 200)^{2} : t^{2} + 400 t + 40000

= \int t^{2} + 400 t + 40000 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 400 t d t + \int 40000 d t

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

\int 400 t d t = 200 t^{2}

\int 40000 d t = 40000 t

= \frac{t ^{3}}{3} + 200 t^{2} + 40000 t

Füge eine Konstante zur Lösung hinzu

= \frac{t ^{3}}{3} + 200 t^{2} + 40000 t + C

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