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Beliebt Rechnen >

integral of (4x^5+10x^3)/(x^2)

Lösung

\int \frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} d x

Lösung

x^{4} + 5 x^{2} + C

Schritte zur Lösung

\int \frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} d x

Multipliziere aus

\frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} : \frac{4 x ^{5}}{x ^{2}} + \frac{10 x ^{3}}{x ^{2}}

Wende die Summenregel an:

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

= \int \frac{4 x ^{5}}{x ^{2}} d x + \int \frac{10 x ^{3}}{x ^{2}} d x

\int \frac{4 x ^{5}}{x ^{2}} d x = x^{4}

\int \frac{10 x ^{3}}{x ^{2}} d x = 5 x^{2}

= x^{4} + 5 x^{2}

Füge eine Konstante zur Lösung hinzu

= x^{4} + 5 x^{2} + C

Graph

Beliebte Beispiele

integral of (3x-5)/(sqrt(x))

\int \frac{3 x - 5}{x} d x

(dy)/(dx)=0.72-(9y)/(1000),y(0)=80

\frac{d y}{d x} = 0.72 - \frac{9 y}{1000}, y (0) = 80

integral from-1 to 1 of x(x^2+9)^3

\int_{- 1}^{1} x (x^{2} + 9)^{3} d x

derivative \sqrt[3]{3+tan(t)}

d er i v a t i v e 3 3 + tan (t)

y(dy)/(dx)+8x^3=4

y \frac{d y}{d x} + 8 x^{3} = 4