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Beliebt Rechnen >

integral of (ln(t)+3t^2-1)

Lösung

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

Lösung

t^{3} + t ln (t) - 2 t + C

Schritte zur Lösung

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

\int ln (t) d t = t ln (t) - t

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

\int 1 d t = t

= t ln (t) - t + t^{3} - t

Vereinfache

= t^{3} + t ln (t) - 2 t

Füge eine Konstante zur Lösung hinzu

= t^{3} + t ln (t) - 2 t + C

Graph

Beliebte Beispiele

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