integral of (ln(x))/(\sqrt[3]{x)}

Lösung

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

\frac{3}{2} x^{\frac{2}{3}} ln (x) - \frac{9}{4} x^{\frac{2}{3}} + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{3}{2 x ^{\frac{1}{3}}} d x = \frac{9}{4} x^{\frac{2}{3}}

= \frac{3}{2} x^{\frac{2}{3}} ln (x) - \frac{9}{4} x^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} x^{\frac{2}{3}} ln (x) - \frac{9}{4} x^{\frac{2}{3}} + C

x \to 0 + lim ((x^{2}) ln (x))

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

d er i v a t i v e y = x - 1

\int \frac{8 x}{x ^{3} + x ^{2} - x - 1} d x

\frac{d}{d x} (- cos (2 x) \cdot 2)