integral of 4xln(x)

Lösung

\int 4 x ln (x) d x

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

Schritte zur Lösung

\int 4 x ln (x) d x

Entferne die Konstante:

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

= 4 \cdot \int x ln (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

y^{^{'}} = x y^{2}

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

a re a 7 cos (7 x), 7 - 7 cos (7 x), [0, \frac{π}{7}]

\frac{d}{d x} (\frac{1}{( 3 x + 1 ) ^{2}})

f^{^{'}} (x) = (3 x^{5} - 2)^{20}