integral of x^3*ln(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

= \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}

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

Füge eine Konstante zur Lösung hinzu

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

\int_{1}^{e} \frac{9 x ^{2} + 9 x + 9}{x} d x

\int \frac{1}{6} d x

\frac{\partial}{\partial x} (6 x^{2} - 4 x y^{2})

d er i v a t i v e f (- 1) = \frac{x + 3}{2}

\frac{\partial}{\partial x} (ln (1 - x - y) - x^{- 1} - y^{- 1})