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Beliebt Rechnen >

integral ln(a^2-x^2)

Lösung

integral

ln (a^{2} - x^{2})

Lösung

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

Schritte zur Lösung

\int ln (a^{2} - x^{2}) d x

Wende die partielle Integration an

= x ln (a^{2} - x^{2}) - \int - \frac{2 x ^{2}}{a ^{2} - x ^{2}} d x

\int - \frac{2 x ^{2}}{a ^{2} - x ^{2}} d x = - a ln \frac{x}{a} + 1 + a ln \frac{x}{a} - 1 + 2 x

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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