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Beliebt Rechnen >

integral of (5-x)/(sqrt(x^2-10x+3))

Lösung

\int \frac{5 - x}{x ^{2} - 10 x + 3} d x

Lösung

- x^{2} - 10 x + 3 + C

Schritte zur Lösung

\int \frac{5 - x}{x ^{2} - 10 x + 3} d x

Multipliziere aus

\frac{5 - x}{x ^{2} - 10 x + 3} : \frac{5}{x ^{2} - 10 x + 3} - \frac{x}{x ^{2} - 10 x + 3}

= \int \frac{5}{x ^{2} - 10 x + 3} - \frac{x}{x ^{2} - 10 x + 3} 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{5}{x ^{2} - 10 x + 3} d x - \int \frac{x}{x ^{2} - 10 x + 3} d x

\int \frac{5}{x ^{2} - 10 x + 3} d x = 5 ln \frac{1}{22} (x^{2} - 10 x + 3) + \frac{1}{22} (x - 5)

\int \frac{x}{x ^{2} - 10 x + 3} d x = x^{2} - 10 x + 3 + 5 ln \frac{1}{22} (x^{2} - 10 x + 3) + \frac{1}{22} (x - 5)

= 5 ln \frac{1}{22} (x^{2} - 10 x + 3) + \frac{1}{22} (x - 5) - (x^{2} - 10 x + 3 + 5 ln \frac{1}{22} (x^{2} - 10 x + 3) + \frac{1}{22} (x - 5))

Vereinfache

= - x^{2} - 10 x + 3

Füge eine Konstante zur Lösung hinzu

= - x^{2} - 10 x + 3 + C

Graph

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