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Beliebt Rechnen >

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

Lösung

\int \frac{( x ^{3} + 4 )}{x ( x ^{2} + 2 )} d x

Lösung

- 2 arctan (\frac{x}{2}) + x - ln x^{2} + 2 + 2 ln (x) + C

Schritte zur Lösung

\int \frac{x ^{3} + 4}{x ( x ^{2} + 2 )} d x

Multipliziere aus

\frac{x ^{3} + 4}{x ( x ^{2} + 2 )} : \frac{x ^{3}}{x ( x ^{2} + 2 )} + \frac{4}{x ( x ^{2} + 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{x ^{3}}{x ( x ^{2} + 2 )} d x + \int \frac{4}{x ( x ^{2} + 2 )} d x

\int \frac{x ^{3}}{x ( x ^{2} + 2 )} d x = - 2 arctan (\frac{x}{2}) + x

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

= - 2 arctan (\frac{x}{2}) + x - ln x^{2} + 2 + 2 ln (x)

Füge eine Konstante zur Lösung hinzu

= - 2 arctan (\frac{x}{2}) + x - ln x^{2} + 2 + 2 ln (x) + C

Graph

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