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Beliebt Rechnen >

integral of (1+t)^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 1 d t = t

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative y=(2x+4)/(1-x)

d er i v a t i v e y = \frac{2 x + 4}{1 - x}

(dN)/(dt)+N=Nte^{t+4}

\frac{d N}{d t} + N = Nt e^{t + 4}

integral from 0 to 1 of x^2e^{x^3}

\int_{0}^{1} x^{2} e^{x^{3}} d x

(dy)/(dx)=-0.5y+x

\frac{d y}{d x} = - 0.5 y + x

limit as x approaches 2pi of 1/(sin(x))

x \to 2 π lim (\frac{1}{sin ( x )})