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Beliebt Rechnen >

integral of t^2(t^3+4)^{-1/2}

Lösung

\int t^{2} (t^{3} + 4)^{- \frac{1}{2}} d t

Lösung

\frac{2}{3} (t^{3} + 4)^{\frac{1}{2}} + C

Schritte zur Lösung

\int t^{2} (t^{3} + 4)^{- \frac{1}{2}} d t

Wende U-Substitution an

= \int \frac{1}{3 u ^{\frac{1}{2}}} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{1}{u ^{\frac{1}{2}}} d u

Wende die Potenzregel an

= \frac{1}{3} \cdot 2 u^{\frac{1}{2}}

Setze in

u = t^{3} + 4

ein

= \frac{1}{3} \cdot 2 (t^{3} + 4)^{\frac{1}{2}}

Vereinfache

\frac{1}{3} \cdot 2 (t^{3} + 4)^{\frac{1}{2}} : \frac{2}{3} (t^{3} + 4)^{\frac{1}{2}}

= \frac{2}{3} (t^{3} + 4)^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} (t^{3} + 4)^{\frac{1}{2}} + C

Graph

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