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Beliebt Rechnen >

integral of (8x+15)ln(2x)

Lösung

\int (8 x + 15) ln (2 x) d x

Lösung

4 x^{2} ln (2 x) + 15 x ln (2 x) - 2 x^{2} - 15 x + C

Schritte zur Lösung

\int (8 x + 15) ln (2 x) d x

Wende die partielle Integration an

= ln (2 x) (4 x^{2} + 15 x) - \int 4 x + 15 d x

\int 4 x + 15 d x = 2 x^{2} + 15 x

= ln (2 x) (4 x^{2} + 15 x) - (2 x^{2} + 15 x)

Vereinfache

ln (2 x) (4 x^{2} + 15 x) - (2 x^{2} + 15 x) : 4 x^{2} ln (2 x) + 15 x ln (2 x) - 2 x^{2} - 15 x

= 4 x^{2} ln (2 x) + 15 x ln (2 x) - 2 x^{2} - 15 x

Füge eine Konstante zur Lösung hinzu

= 4 x^{2} ln (2 x) + 15 x ln (2 x) - 2 x^{2} - 15 x + C

Graph

Beliebte Beispiele

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\int t^{2} e^{- 9 t} d t

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