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Beliebt Rechnen >

integral of (x+x^2-x^3)/(2e^4x^2)

Lösung

\int \frac{x + x ^{2} - x ^{3}}{2 e ^{4} x ^{2}} d x

Lösung

\frac{1}{2 e ^{4}} (ln ∣ x ∣ + x - \frac{x ^{2}}{2}) + C

Schritte zur Lösung

\int \frac{x + x ^{2} - x ^{3}}{2 e ^{4} x ^{2}} d x

Entferne die Konstante:

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

= \frac{1}{2 e ^{4}} \cdot \int \frac{x + x ^{2} - x ^{3}}{x ^{2}} d x

Multipliziere aus

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

= \frac{1}{2 e ^{4}} \cdot \int \frac{1}{x} + 1 - 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

= \frac{1}{2 e ^{4}} (\int \frac{1}{x} d x + \int 1 d x - \int x d x)

\int \frac{1}{x} d x = ln ∣ x ∣

\int 1 d x = x

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

= \frac{1}{2 e ^{4}} (ln ∣ x ∣ + x - \frac{x ^{2}}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2 e ^{4}} (ln ∣ x ∣ + x - \frac{x ^{2}}{2}) + C

Graph

Beliebte Beispiele

integral of (3x+5)/((x+1)(x-1)^2)

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

integral of 1/(sqrt(20+x^2))

\int \frac{1}{20 + x ^{2}} d x

integral of y^4ln(sqrt(y))

\int y^{4} ln (y) d y

integral of 1/(xln(x)ln^2(ln(x)))

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

integral of (0.1q+1)e^{0.3q}

\int (0.1 q + 1) e^{0.3 q} d q