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Beliebt Rechnen >

integral of ((3x+5))/(x^2+2x+1)

Lösung

\int \frac{( 3 x + 5 )}{x ^{2} + 2 x + 1} d x

Lösung

3 ln ∣ x + 1 ∣ - \frac{2}{x + 1} + C

Schritte zur Lösung

\int \frac{3 x + 5}{x ^{2} + 2 x + 1} d x

Vervollständige das Quadrat

x^{2} + 2 x + 1 : (x + 1)^{2}

= \int \frac{3 x + 5}{( x + 1 ) ^{2}} d x

Wende U-Substitution an

= \int \frac{3 u + 2}{u ^{2}} d u

Multipliziere aus

\frac{3 u + 2}{u ^{2}} : \frac{3}{u} + \frac{2}{u ^{2}}

= \int \frac{3}{u} + \frac{2}{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{3}{u} d u + \int \frac{2}{u ^{2}} d u

\int \frac{3}{u} d u = 3 ln ∣ u ∣

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

= 3 ln ∣ u ∣ - \frac{2}{u}

Setze in

u = x + 1

ein

= 3 ln ∣ x + 1 ∣ - \frac{2}{x + 1}

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x + 1 ∣ - \frac{2}{x + 1} + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(x+4)

\frac{\partial}{\partial x} (x + 4)

limit as x approaches 5 of-x^2+9x-7

x \to 5 lim (- x^{2} + 9 x - 7)

derivative of (3x^5-1^7)

\frac{d}{d x} ((3 x^{5} - 1)^{7})

integral of (e^u)/((3-e^u)^2)

\int \frac{e ^{u}}{( 3 - e ^{u} ) ^{2}} d u

laplacetransform e^{(,\at)}

l a pl a ce t r an s f or m e^{(, at)}