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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 6/(sqrt(x^2+16))

\int \frac{6}{x ^{2} + 16} d x

derivative of ln(3x^2-2x)

\frac{d}{d x} (ln (3 x^{2} - 2 x))

derivative ln(15)

d er i v a t i v e ln (15)

integral from 0 to 4 of 1/(sqrt(16+t^2))

\int_{0}^{4} \frac{1}{16 + t ^{2}} d t

integral of 8x(4x^2-3)^5

\int 8 x (4 x^{2} - 3)^{5} d x