integral of (x-1)ln(x)

Lösung

\int (x - 1) ln (x) d x

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

Schritte zur Lösung

\int (x - 1) ln (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (- f (r, x) r sin (x) \cdot sin (x))

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\frac{d}{d x} (- e^{- x} cos (x) - e^{- x} sin (x))

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

\int e^{1 - 2 t} d t