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

Lösung

integral

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

x - ln ∣ x - 1 ∣ + 4 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int 1 d x = x

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

\int \frac{4}{x - 2} d x = 4 ln ∣ x - 2 ∣

= x - ln ∣ x - 1 ∣ + 4 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= x - ln ∣ x - 1 ∣ + 4 ln ∣ x - 2 ∣ + C

in t e g r a l \frac{1}{( x ^{2} + 2 x ) ^{\frac{1}{2}}}

in t e g r a l \frac{( x + 2 )}{( x ^{2} + 3 x )}

in t e g r a l \frac{v}{2}

in t e g r a l \frac{( x - 1 )}{( x ^{2} + 2 x + 3 )}

in t e g r a l \frac{1}{x ( x ^{2} - 1 )}