integral of 2xln(x)

Lösung

\int 2 \cdot x \cdot ln (x) d x

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

Schritte zur Lösung

\int 2 x ln (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int x ln (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial y} (- \frac{1}{2} x - 3 y + 1)

\int u cos (u) d u

sin (x) sin (y) d x + cos (x) cos (y) d y = 0

\frac{\partial}{\partial y} (x^{2} e^{2 y})

x \to 4 - lim (\frac{2 x}{16 - x ^{2}})