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Beliebt Rechnen >

integral of [ln(x+sqrt(1+x^2))]^2

Lösung

\int [ln (x + 1 + x^{2})]^{2} d x

Lösung

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

Schritte zur Lösung

\int [ln (x + 1 + x^{2})]^{2} d x

Vereinfache

= \int ln^{2} (x + 1 + x^{2}) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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