integral of 2x^3ln(x)

Lösung

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

2 (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= 2 (\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x)

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= 2 (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16})

Füge eine Konstante zur Lösung hinzu

= 2 (\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}) + C

\int \frac{5}{9 + x ^{2}} d x

\int \frac{cos ( ln ( t ) )}{4 t} d t

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

\int sec^{10} (6 x) tan^{3} (6 x) d x

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