integral (ln(1+x^2))/(x^2)

Lösung

integral

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

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

Schritte zur Lösung

\int \frac{ln ( 1 + x ^{2} )}{x ^{2}} d x

Wende die partielle Integration an

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

\int - \frac{2}{1 + x ^{2}} d x = - 2 arctan (x)

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

in t e g r a l \frac{x}{( x ^{2} + 1 ) ^{\frac{1}{3}}}

in t e g r a l 2^{2 x}

in t e g r a l \frac{( x ^{4} )}{( x ^{5} + x )}

in t e g r a l x^{2} + 2

in t e g r a l \frac{2 x}{( 2 x + 1 )}