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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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