integral of (ln(x^2))/(x^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

\frac{ln ( x ^{2} )}{2 x ^{2}} = \frac{ln ( x )}{x ^{2}}

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

Füge eine Konstante zur Lösung hinzu

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

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

\int cos (2 t) + sin (2 t) d t

d er i v a t i v e x (7^{- 3 x})

x \to 2 lim (16)

ma c l a u r in cos (3 x)