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Beliebt Rechnen >

integral of (4x+3)(ln(2x-3))

Lösung

\int (4 x + 3) (ln (2 x - 3)) d x

Lösung

2 x^{2} ln (2 x - 3) + 3 x ln (2 x - 3) - x^{2} - 6 x - 9 ln ∣ 2 x - 3 ∣ + \frac{9}{2} + C

Schritte zur Lösung

\int (4 x + 3) ln (2 x - 3) d x

Wende die partielle Integration an

= ln (2 x - 3) (2 x^{2} + 3 x) - \int \frac{2 ( 2 x ^{2} + 3 x )}{2 x - 3} d x

\int \frac{2 ( 2 x ^{2} + 3 x )}{2 x - 3} d x = x^{2} + 6 x + 9 ln ∣ 2 x - 3 ∣ - \frac{9}{2}

= ln (2 x - 3) (2 x^{2} + 3 x) - (x^{2} + 6 x + 9 ln ∣ 2 x - 3 ∣ - \frac{9}{2})

Vereinfache

ln (2 x - 3) (2 x^{2} + 3 x) - (x^{2} + 6 x + 9 ln ∣ 2 x - 3 ∣ - \frac{9}{2}) : 2 x^{2} ln (2 x - 3) + 3 x ln (2 x - 3) - x^{2} - 6 x - 9 ln ∣ 2 x - 3 ∣ + \frac{9}{2}

= 2 x^{2} ln (2 x - 3) + 3 x ln (2 x - 3) - x^{2} - 6 x - 9 ln ∣ 2 x - 3 ∣ + \frac{9}{2}

Füge eine Konstante zur Lösung hinzu

= 2 x^{2} ln (2 x - 3) + 3 x ln (2 x - 3) - x^{2} - 6 x - 9 ln ∣ 2 x - 3 ∣ + \frac{9}{2} + C

Graph

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