integral of ((4x-7))/(x^2-6x+13)

Lösung

\int \frac{( 4 x - 7 )}{x ^{2} - 6 x + 13} d x

\frac{5}{2} arctan (\frac{1}{2} (x - 3)) + 2 ln x^{2} - 6 x + 13 + C

Schritte zur Lösung

\int \frac{4 x - 7}{x ^{2} - 6 x + 13} d x

Wende die partielle Integration an

= \frac{1}{2} arctan (\frac{1}{2} (x - 3)) (4 x - 7) - \int 2 arctan (\frac{1}{2} (x - 3)) d x

\int 2 arctan (\frac{1}{2} (x - 3)) d x = 2 (x arctan (\frac{1}{2} (x - 3)) - ln x^{2} - 6 x + 13 - 3 arctan (\frac{1}{2} (x - 3)))

= \frac{1}{2} arctan (\frac{1}{2} (x - 3)) (4 x - 7) - 2 (x arctan (\frac{1}{2} (x - 3)) - ln x^{2} - 6 x + 13 - 3 arctan (\frac{1}{2} (x - 3)))

Vereinfache

\frac{1}{2} arctan (\frac{1}{2} (x - 3)) (4 x - 7) - 2 (x arctan (\frac{1}{2} (x - 3)) - ln x^{2} - 6 x + 13 - 3 arctan (\frac{1}{2} (x - 3))) : \frac{5}{2} arctan (\frac{1}{2} (x - 3)) + 2 ln x^{2} - 6 x + 13

= \frac{5}{2} arctan (\frac{1}{2} (x - 3)) + 2 ln x^{2} - 6 x + 13

Füge eine Konstante zur Lösung hinzu

= \frac{5}{2} arctan (\frac{1}{2} (x - 3)) + 2 ln x^{2} - 6 x + 13 + C

d er i v a t i v e - \frac{7}{x ^{2}}

(x^{2} + 4) d y = (2 x - 8 x y) d x

\int - \frac{2}{πn} cos (\frac{πn}{2} x) d x

\frac{d y}{d x} = \frac{7 x ^{2}}{5 y ^{2}}

d er i v a t i v e f (x) = (\frac{( x + 1 )}{( x - 1 )})^{2}