integral of (x+6)/((x+1)^2)

Lösung

\int \frac{x + 6}{( x + 1 ) ^{2}} d x

ln ∣ x + 1 ∣ - \frac{5}{x + 1} + C

Schritte zur Lösung

\int \frac{x + 6}{( x + 1 ) ^{2}} d x

Wende U-Substitution an

= \int \frac{u + 5}{u ^{2}} d u

Multipliziere aus

\frac{u + 5}{u ^{2}} : \frac{1}{u} + \frac{5}{u ^{2}}

= \int \frac{1}{u} + \frac{5}{u ^{2}} 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 \frac{1}{u} d u + \int \frac{5}{u ^{2}} d u

\int \frac{1}{u} d u = ln ∣ u ∣

\int \frac{5}{u ^{2}} d u = - \frac{5}{u}

= ln ∣ u ∣ - \frac{5}{u}

Setze in

u = x + 1

ein

= ln ∣ x + 1 ∣ - \frac{5}{x + 1}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 1 ∣ - \frac{5}{x + 1} + C

\frac{\partial ^{2}}{\partial r \partial θ} (r (θ) cos (θ))

x \to 0 lim (\frac{x ^{2} + 1}{x - 1})

(x + y + 1) d x - (y - x + 3) d y = 0

x \to - 1 lim (7 ∣ x + 1 ∣ - 4)

\int e^{2 x} d x