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Beliebt Rechnen >

integral of (xln(x))/(sqrt(x^2-4))

Lösung

\int \frac{x ln ( x )}{x ^{2} - 4} d x

Lösung

ln (x) x^{2} - 4 + 2 arcsec (\frac{1}{2} x) - x^{2} - 4 + C

Schritte zur Lösung

\int \frac{x ln ( x )}{x ^{2} - 4} d x

\frac{x ln ( x )}{x ^{2} - 4} = x ln (x) \frac{1}{x ^{2} - 4}

= \int x ln (x) \frac{1}{x ^{2} - 4} d x

Wende die partielle Integration an

= ln (x) x^{2} - 4 - \int \frac{x ^{2} - 4}{x} d x

\int \frac{x ^{2} - 4}{x} d x = - 2 arcsec (\frac{1}{2} x) + x^{2} - 4

= ln (x) x^{2} - 4 - (- 2 arcsec (\frac{1}{2} x) + x^{2} - 4)

Vereinfache

= ln (x) x^{2} - 4 + 2 arcsec (\frac{1}{2} x) - x^{2} - 4

Füge eine Konstante zur Lösung hinzu

= ln (x) x^{2} - 4 + 2 arcsec (\frac{1}{2} x) - x^{2} - 4 + C

Graph

Beliebte Beispiele

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\int \frac{12 x ^{3}}{( 3 x ^{4} - 4 ) ln ( 3 x ^{4} - 4 )} d x

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\int 324 - 9 x^{2} d x