integral of (sqrt(t^3)+\sqrt[3]{t^2})

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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