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Beliebt Rechnen >

integral of (9x+2)(3x-5)

Lösung

\int (9 x + 2) (3 x - 5) d x

Lösung

9 x^{3} - \frac{39 x ^{2}}{2} - 10 x + C

Schritte zur Lösung

\int (9 x + 2) (3 x - 5) d x

Multipliziere aus

(9 x + 2) (3 x - 5) : 27 x^{2} - 39 x - 10

= \int 27 x^{2} - 39 x - 10 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 27 x^{2} d x - \int 39 x d x - \int 10 d x

\int 27 x^{2} d x = 9 x^{3}

\int 39 x d x = \frac{39 x ^{2}}{2}

\int 10 d x = 10 x

= 9 x^{3} - \frac{39 x ^{2}}{2} - 10 x

Füge eine Konstante zur Lösung hinzu

= 9 x^{3} - \frac{39 x ^{2}}{2} - 10 x + C

Graph

Beliebte Beispiele

integral of (e^{5x}-5/x)

\int (e^{5 x} - \frac{5}{x}) d x

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integral of (7x+19)/((x-3)(x+5))

\int \frac{7 x + 19}{( x - 3 ) ( x + 5 )} d x

integral of (x^2)/((2x-1)^2)

\int \frac{x ^{2}}{( 2 x - 1 ) ^{2}} d x