integral of xln(x))

Lösung

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

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

Schritte zur Lösung

\int x d ln (x) d x

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{x}{5 + x} d x

\frac{d}{d x} (\frac{( 5 x - 3 )}{4 x - \frac{3}{x}})

\frac{d}{d x} (sin^{5} ((x^{2} + 1)^{7}))

\int 6 x cos (x^{2}) d x

\frac{\partial}{\partial x} (x^{8} + 5 x y^{9})