integral x/((x+1))

Lösung

integral

\frac{x}{( x + 1 )}

x + 1 - ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{x}{x + 1} d x

Wende U-Substitution an

= \int \frac{u - 1}{u} d u

Multipliziere aus

\frac{u - 1}{u} : 1 - \frac{1}{u}

= \int 1 - \frac{1}{u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u - \int \frac{1}{u} d u

\int 1 d u = u

\int \frac{1}{u} d u = ln ∣ u ∣

= u - ln ∣ u ∣

Setze in

u = x + 1

ein

= x + 1 - ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= x + 1 - ln ∣ x + 1 ∣ + C

in t e g r a l 3 x^{3}

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

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

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

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