integral of-2x*ln(x)

Lösung

\int - 2 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

t an g e n t x^{2} - \frac{1}{x}

\int_{3}^{6} \frac{2 x - 3}{6} d x

\int_{0}^{π} x \cdot sin^{2} (x) d x

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

\int \frac{( 3 x ^{2} )}{2} d x