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Beliebt Rechnen >

integral of log_{e}(1+x^2)

Lösung

\int lo g_{e} (1 + x^{2}) d x

Lösung

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

Schritte zur Lösung

\int lo g_{e} (1 + x^{2}) d x

Wende die log Regel an:

lo g_{e} (x) = ln (x)

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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