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Beliebt Rechnen >

integral of (2-t)sqrt(t)

Lösung

\int (2 - t) t d t

Lösung

\frac{4}{3} t^{\frac{3}{2}} - \frac{2}{5} t^{\frac{5}{2}} + C

Schritte zur Lösung

\int (2 - t) t d t

Multipliziere aus

(2 - t) t : 2 t - t^{\frac{3}{2}}

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

\int 2 t d t = \frac{4}{3} t^{\frac{3}{2}}

\int t^{\frac{3}{2}} d t = \frac{2}{5} t^{\frac{5}{2}}

= \frac{4}{3} t^{\frac{3}{2}} - \frac{2}{5} t^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} t^{\frac{3}{2}} - \frac{2}{5} t^{\frac{5}{2}} + C

Graph

Beliebte Beispiele

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\int \frac{( lo g _{10} ( x ) )}{x} d x