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

Lösung

integral

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

in t e g r a l a + 3 c - 2 d

in t e g r a l (1 - 0.1 x)^{- 2}

in t e g r a l \frac{( 5 x - 6 )}{( x ^{2} - 2 x + 2 )}

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

in t e g r a l ln ((\frac{1}{x}) - 1)