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Beliebt Rechnen >

integral of sqrt(t)(t^2+t-1)

Lösung

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

Lösung

t (\frac{t ^{3}}{3} + \frac{t ^{2}}{2} - t) - \frac{1}{210} t^{\frac{3}{2}} (10 t^{2} + 21 t - 70) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= t (\frac{t ^{3}}{3} + \frac{t ^{2}}{2} - t) - \int \frac{1}{12} t (2 t^{2} + 3 t - 6) d t

\int \frac{1}{12} t (2 t^{2} + 3 t - 6) d t = \frac{1}{210} t^{\frac{3}{2}} (10 t^{2} + 21 t - 70)

= t (\frac{t ^{3}}{3} + \frac{t ^{2}}{2} - t) - \frac{1}{210} t^{\frac{3}{2}} (10 t^{2} + 21 t - 70)

Füge eine Konstante zur Lösung hinzu

= t (\frac{t ^{3}}{3} + \frac{t ^{2}}{2} - t) - \frac{1}{210} t^{\frac{3}{2}} (10 t^{2} + 21 t - 70) + C

Graph

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