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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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x \to 1 lim (\frac{x ^{2} - 4}{x - 2})

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\int (\frac{6}{x} + \frac{x}{6}) d x

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