integral of sqrt(t)*ln(t)

Lösung

\int t \cdot 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 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

t an g e n t 2 x^{3} - 3 x^{2} - 72 x + 2

in v erse l a pl a ce \frac{s + 1}{s ^{2} - 4 s}

d er i v a t i v e 2 \cdot e^{x^{2} - 4 x}

\int 2 x - 5 d x

\frac{d}{d x} (x ln (x^{2} + 4) + 4 arctan (\frac{x}{2}) - 2 x)