integral of (4x-8)/(x^2-4x+5)

Lösung

\int \frac{4 x - 8}{x ^{2} - 4 x + 5} d x

2 ln x^{2} - 4 x + 5 + C

Schritte zur Lösung

\int \frac{4 x - 8}{x ^{2} - 4 x + 5} d x

Wende die partielle Integration an

= (4 x - 8) arctan (x - 2) - \int 4 arctan (x - 2) d x

\int 4 arctan (x - 2) d x = 4 (x arctan (x - 2) - \frac{1}{2} ln x^{2} - 4 x + 5 - 2 arctan (x - 2))

= (4 x - 8) arctan (x - 2) - 4 (x arctan (x - 2) - \frac{1}{2} ln x^{2} - 4 x + 5 - 2 arctan (x - 2))

Vereinfache

(4 x - 8) arctan (x - 2) - 4 (x arctan (x - 2) - \frac{1}{2} ln x^{2} - 4 x + 5 - 2 arctan (x - 2)) : 2 ln x^{2} - 4 x + 5

= 2 ln x^{2} - 4 x + 5

Füge eine Konstante zur Lösung hinzu

= 2 ln x^{2} - 4 x + 5 + C

\int x^{2} (7 x^{3} - 3)^{8} d x

\int \frac{1}{1 + cos ( x ) + 7 sin ( x )} d x

\int (\frac{7 - x}{- 3}) d x

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

\int x e^{3 x + 5} d x