integral of t^{1/2}ln(t)

Lösung

\int t^{\frac{1}{2}} ln (t) d t

\frac{2}{3} t^{\frac{3}{2}} ln (t) - \frac{4}{9} t^{\frac{3}{2}} + C

Schritte zur Lösung

\int t^{\frac{1}{2}} ln (t) d t

Wende die partielle Integration an

= \frac{2}{3} t^{\frac{3}{2}} ln (t) - \int \frac{2}{3} t^{\frac{1}{2}} d t

\int \frac{2}{3} t^{\frac{1}{2}} d t = \frac{4}{9} t^{\frac{3}{2}}

= \frac{2}{3} t^{\frac{3}{2}} ln (t) - \frac{4}{9} t^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} t^{\frac{3}{2}} ln (t) - \frac{4}{9} t^{\frac{3}{2}} + C

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