integral of-x*ln(x)

Lösung

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

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

Schritte zur Lösung

\int - x ln (x) d x

Entferne die Konstante:

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

= - \int x ln (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{1}{1 + 16 x ^{2}} d x

d er i v a t i v e x^{3} cos (x^{2})

\int \frac{x ^{2}}{25 - 9 x ^{2}} d x

2 y^{^{''}} - 9 y^{^{'}} - 5 y = 0

d er i v a t i v e sec^{2} (π x)