integral of 5/(sqrt(11-11x^2))

Lösung

\int \frac{5}{11 - 11 x ^{2}} d x

5 (\frac{x}{11 - 11 x ^{2}} - \frac{1}{11} (- arcsin (x) + \frac{x}{1 - x ^{2}})) + C

Schritte zur Lösung

\int \frac{5}{11 - 11 x ^{2}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{1}{11 - 11 x ^{2}} d x

Wende die partielle Integration an

= 5 (\frac{x}{11 - 11 x ^{2}} - \int \frac{11 x ^{2}}{( 11 - 11 x ^{2} ) ^{\frac{3}{2}}} d x)

\int \frac{11 x ^{2}}{( 11 - 11 x ^{2} ) ^{\frac{3}{2}}} d x = \frac{1}{11} (- arcsin (x) + \frac{x}{1 - x ^{2}})

= 5 (\frac{x}{11 - 11 x ^{2}} - \frac{1}{11} (- arcsin (x) + \frac{x}{1 - x ^{2}}))

Füge eine Konstante zur Lösung hinzu

= 5 (\frac{x}{11 - 11 x ^{2}} - \frac{1}{11} (- arcsin (x) + \frac{x}{1 - x ^{2}})) + C

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