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Beliebt Rechnen >

integral ln(x^2+1)+6

Lösung

integral

ln (x^{2} + 1) + 6

Lösung

x ln (x^{2} + 1) + 2 arctan (x) + 4 x + C

Schritte zur Lösung

\int ln (x^{2} + 1) + 6 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int ln (x^{2} + 1) d x + \int 6 d x

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

\int 6 d x = 6 x

= x ln (x^{2} + 1) - 2 (- arctan (x) + x) + 6 x

Vereinfache

x ln (x^{2} + 1) - 2 (- arctan (x) + x) + 6 x : x ln (x^{2} + 1) + 2 arctan (x) + 4 x

= x ln (x^{2} + 1) + 2 arctan (x) + 4 x

Füge eine Konstante zur Lösung hinzu

= x ln (x^{2} + 1) + 2 arctan (x) + 4 x + C

Graph

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