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Beliebt Rechnen >

integral of ((arctan(ln(x+3))))/(x+3)

Lösung

\int \frac{( arctan ( ln ( x + 3 ) ) )}{x + 3} d x

Lösung

ln (x + 3) arctan (ln (x + 3)) - \frac{1}{2} ln ln^{2} (x + 3) + 1 + C

Schritte zur Lösung

\int \frac{arctan ( ln ( x + 3 ) )}{x + 3} d x

Wende U-Substitution an

= \int \frac{arctan ( ln ( u ) )}{u} d u

Wende U-Substitution an

= \int arctan (v) d v

Wende die partielle Integration an

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

\int \frac{v}{v ^{2} + 1} d v = \frac{1}{2} ln v^{2} + 1

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

Ersetze zurück

= ln (x + 3) arctan (ln (x + 3)) - \frac{1}{2} ln ln^{2} (x + 3) + 1

Füge eine Konstante zur Lösung hinzu

= ln (x + 3) arctan (ln (x + 3)) - \frac{1}{2} ln ln^{2} (x + 3) + 1 + C

Graph

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