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

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int (12 x) d x

\int - cos (t) d t

d er i v a t i v e f (x) = arcsec (5 x)

\int x os (2 x) d x

\frac{d}{d x} (a sin (b x + c) + d)