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Beliebt Rechnen >

integral of (x+3x^2+x^3)/(x^2)

Lösung

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

Lösung

ln ∣ x ∣ + 3 x + \frac{x ^{2}}{2} + C

Schritte zur Lösung

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

Vereinfache

\frac{x + 3 x ^{2} + x ^{3}}{x ^{2}} : \frac{1 + 3 x + x ^{2}}{x}

= \int \frac{1 + 3 x + x ^{2}}{x} d x

Multipliziere aus

\frac{1 + 3 x + x ^{2}}{x} : \frac{1}{x} + 3 + x

= \int \frac{1}{x} + 3 + x 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 \frac{1}{x} d x + \int 3 d x + \int x d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int 3 d x = 3 x

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

= ln ∣ x ∣ + 3 x + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ + 3 x + \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

integral of (x^2+43)/(x^2+49)

\int \frac{x ^{2} + 43}{x ^{2} + 49} d x

integral of 1/(x^2-6x+25)

\int \frac{1}{x ^{2} - 6 x + 25} d x

integral of x/(x^2-4x-5)

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

integral of (tarctan(t))/(sqrt(1+t^2))

\int \frac{t arctan ( t )}{1 + t ^{2}} d t

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

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