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Beliebt Rechnen >

integral of ((4x-5)(2x-7))/3

Lösung

\int \frac{( 4 x - 5 ) ( 2 x - 7 )}{3} d x

Lösung

\frac{1}{9} (8 x^{3} - 57 x^{2} + 105 x) + C

Schritte zur Lösung

\int \frac{( 4 x - 5 ) ( 2 x - 7 )}{3} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int (4 x - 5) (2 x - 7) d x

Wende die partielle Integration an

= \frac{1}{3} ((2 x - 7) (2 x^{2} - 5 x) - \int 2 (2 x^{2} - 5 x) d x)

\int 2 (2 x^{2} - 5 x) d x = \frac{4 x ^{3}}{3} - 5 x^{2}

= \frac{1}{3} ((2 x - 7) (2 x^{2} - 5 x) - (\frac{4 x ^{3}}{3} - 5 x^{2}))

Vereinfache

\frac{1}{3} ((2 x - 7) (2 x^{2} - 5 x) - (\frac{4 x ^{3}}{3} - 5 x^{2})) : \frac{1}{9} (8 x^{3} - 57 x^{2} + 105 x)

= \frac{1}{9} (8 x^{3} - 57 x^{2} + 105 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9} (8 x^{3} - 57 x^{2} + 105 x) + C

Graph

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