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Beliebt Rechnen >

integral of t\sqrt[3]{t+10}

Lösung

\int t 3 t + 10 d t

Lösung

\frac{3}{7} (t + 10)^{\frac{7}{3}} - \frac{15}{2} (t + 10)^{\frac{4}{3}} + C

Schritte zur Lösung

\int t 3 t + 10 d t

Wende U-Substitution an

= \int (u - 10) 3 u d u

Multipliziere aus

(u - 10) 3 u : u^{\frac{4}{3}} - 10 3 u

= \int u^{\frac{4}{3}} - 10 3 u d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{\frac{4}{3}} d u - \int 10 3 u d u

\int u^{\frac{4}{3}} d u = \frac{3}{7} u^{\frac{7}{3}}

\int 10 3 u d u = \frac{15}{2} u^{\frac{4}{3}}

= \frac{3}{7} u^{\frac{7}{3}} - \frac{15}{2} u^{\frac{4}{3}}

Setze in

u = t + 10

ein

= \frac{3}{7} (t + 10)^{\frac{7}{3}} - \frac{15}{2} (t + 10)^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{7} (t + 10)^{\frac{7}{3}} - \frac{15}{2} (t + 10)^{\frac{4}{3}} + C

Graph

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