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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

= \int x^{2} - 3 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 x^{2} d x - \int 3 x d x - \int 10 d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 10 d x = 10 x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of e^{(x^4/(10)})

\frac{d}{d x} (e^{\frac{x ^{4}}{10}})

(dy)/(dx)=x^2+y-1

\frac{d y}{d x} = x^{2} + y - 1

y^{''}+9y=2sin(2x),y(0)=0,y^'(0)=-1

y^{^{''}} + 9 y = 2 sin (2 x), y (0) = 0, y^{^{'}} (0) = - 1

tangent (4x)/((x^2+1))

t an g e n t \frac{4 x}{( x ^{2} + 1 )}

integral from 0 to 3 of (1+6x^2-10x^4)

\int_{0}^{3} (1 + 6 x^{2} - 10 x^{4}) d x