integral from 0 to 2x^2 of xln(x)

Lösung

\int_{0}^{2 x^{2}} x ln (x) d x

2 x^{4} ln (2 x^{2}) - x^{4}

Schritte zur Lösung

\int_{0}^{2 x^{2}} x ln (x) d x

Wende die partielle Integration an

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{2 x^{2}}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{2 x^{2}}

Berechne die Grenzen:

2 x^{4} (ln (2) + 2 ln (x)) - x^{4}

= 2 x^{4} (ln (2) + 2 ln (x)) - x^{4}

Vereinfache

= 2 x^{4} ln (2 x^{2}) - x^{4}

\int_{2}^{x} arctan (t) d t

\int_{8}^{64} 3 x d x

\int_{0.1}^{2} t^{2} e^{3 t} d t

\int_{0}^{r} 9 e^{x} d x

\int_{- 2}^{2} e^{4 x} d x