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Beliebt Rechnen >

integral of ln(e^{(2t-1)})

Lösung

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

Lösung

t^{2} - t + C

Schritte zur Lösung

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

Vereinfache

ln (e^{2 t - 1}) : 2 t - 1

= \int 2 t - 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 2 t d t - \int 1 d t

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

\int 1 d t = t

= t^{2} - t

Füge eine Konstante zur Lösung hinzu

= t^{2} - t + C

Graph

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