integral of (x^2)/(2x-x^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{1}{a x - x ^{2}} d x

\int \frac{1}{x ^{2} - a x} d x

\int 2 x (x + x) d x

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

\int \frac{1}{x e ^{x}} d x