integral of ((x-2))/(sqrt(x^2-6x))

Lösung

\int \frac{( x - 2 )}{x ^{2} - 6 x} d x

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

Schritte zur Lösung

\int \frac{x - 2}{x ^{2} - 6 x} d x

Multipliziere aus

\frac{x - 2}{x ^{2} - 6 x} : \frac{x}{x ^{2} - 6 x} - \frac{2}{x ^{2} - 6 x}

= \int \frac{x}{x ^{2} - 6 x} - \frac{2}{x ^{2} - 6 x} 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 \frac{x}{x ^{2} - 6 x} d x - \int \frac{2}{x ^{2} - 6 x} d x

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{4}{64 - 16 x ^{2}} d x

\int \frac{x ^{3} + x}{( x ^{2} + 1 ) ^{2}} d x

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\int \frac{2 x + 1}{x ^{2} - 4 x + 5} d x

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