integral of xln(x)-x

Lösung

\int x ln (x) - x d x

\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4} - \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int x ln (x) - x 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 x ln (x) d x - \int x d x

\int x ln (x) d x = \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}

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

= \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4} - \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4} - \frac{x ^{2}}{2} + C

\int_{0}^{1} x^{\frac{1}{3}} - x^{3} d x

\int cos (3 x) cos (2 x) cos (x) d x

y^{^{'}} = \frac{( 6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2} )}{x ^{3} y}

n = 0 \sum \infty \frac{1}{( n ^{2} - 1 )}

x \to 1 - lim (- \frac{2}{1 - x})