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Beliebt Rechnen >

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

Lösung

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

Lösung

2 ln ∣ x ∣ - 5 arctan (x) + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{2 x ^{2} - 5 x + 2}{x ^{3} + x} : \frac{2}{x} - \frac{5}{x ^{2} + 1}

= \int \frac{2}{x} - \frac{5}{x ^{2} + 1} 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{2}{x} d x - \int \frac{5}{x ^{2} + 1} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{5}{x ^{2} + 1} d x = 5 arctan (x)

= 2 ln ∣ x ∣ - 5 arctan (x)

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ - 5 arctan (x) + C

Graph

Beliebte Beispiele

integral of 1/(sqrt(3-x^2+4x))

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

f(t)=cos(t)+tsin(t)

f (t) = cos (t) + t sin (t)

derivative of 1/((x+k^3))

\frac{d}{d x} (\frac{1}{( x + k ) ^{3}})

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

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

inverselaplace 2/(s^2-s)

in v erse l a pl a ce \frac{2}{s ^{2} - s}