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Beliebt Rechnen >

integral of (x^2+17)/(sqrt(x^2+9))

Lösung

\int \frac{x ^{2} + 17}{x ^{2} + 9} d x

Lösung

9 (- \frac{1}{2} ln (\frac{x + 9 + x ^{2}}{3}) + \frac{1}{18} x 9 + x^{2}) + 17 ln (\frac{1}{3} x + 9 + x^{2}) + C

Schritte zur Lösung

\int \frac{x ^{2} + 17}{x ^{2} + 9} d x

Multipliziere aus

\frac{x ^{2} + 17}{x ^{2} + 9} : \frac{x ^{2}}{x ^{2} + 9} + \frac{17}{x ^{2} + 9}

= \int \frac{x ^{2}}{x ^{2} + 9} + \frac{17}{x ^{2} + 9} 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 ^{2}}{x ^{2} + 9} d x + \int \frac{17}{x ^{2} + 9} d x

\int \frac{x ^{2}}{x ^{2} + 9} d x = 9 (- \frac{1}{2} ln (\frac{x + 9 + x ^{2}}{3}) + \frac{1}{18} x 9 + x^{2})

\int \frac{17}{x ^{2} + 9} d x = 17 ln (\frac{1}{3} x + 9 + x^{2})

= 9 (- \frac{1}{2} ln (\frac{x + 9 + x ^{2}}{3}) + \frac{1}{18} x 9 + x^{2}) + 17 ln (\frac{1}{3} x + 9 + x^{2})

Füge eine Konstante zur Lösung hinzu

= 9 (- \frac{1}{2} ln (\frac{x + 9 + x ^{2}}{3}) + \frac{1}{18} x 9 + x^{2}) + 17 ln (\frac{1}{3} x + 9 + x^{2}) + C

Graph

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