integral of (2t^{2/3}+sqrt(t))

Lösung

\int (2 t^{\frac{2}{3}} + t) d t

\frac{6}{5} t^{\frac{5}{3}} + \frac{2}{3} t^{\frac{3}{2}} + C

Schritte zur Lösung

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

\int 2 t^{\frac{2}{3}} d t = \frac{6}{5} t^{\frac{5}{3}}

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

= \frac{6}{5} t^{\frac{5}{3}} + \frac{2}{3} t^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{6}{5} t^{\frac{5}{3}} + \frac{2}{3} t^{\frac{3}{2}} + C

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