integral of ((ln(x))/(x^3))

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int_{0}^{1} \frac{x}{e ^{x}} d x

\frac{d x}{d t} = x^{2} + \frac{1}{49}

\frac{\partial}{\partial x} (ln (x y) + x e^{y})

\int \frac{2 x}{u}

t \to 1 lim (t^{\frac{1}{t - 1}})