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Beliebt Rechnen >

integral of ln(2+t^2)

Lösung

\int ln (2 + t^{2}) d t

Lösung

t ln (2 + t^{2}) + 22 arctan (\frac{t}{2}) - 2 t + C

Schritte zur Lösung

\int ln (2 + t^{2}) d t

Wende die partielle Integration an

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

\int \frac{2 t ^{2}}{2 + t ^{2}} d t = - 22 arctan (\frac{t}{2}) + 2 t

= t ln (2 + t^{2}) - (- 22 arctan (\frac{t}{2}) + 2 t)

Vereinfache

= t ln (2 + t^{2}) + 22 arctan (\frac{t}{2}) - 2 t

Füge eine Konstante zur Lösung hinzu

= t ln (2 + t^{2}) + 22 arctan (\frac{t}{2}) - 2 t + C

Graph

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