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Beliebt Rechnen >

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

Lösung

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

Lösung

x + 2 - 4 ln ∣ x + 2 ∣ - \frac{9}{x + 2} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{2} + 5}{( x + 2 ) ^{2}} : \frac{x ^{2}}{( x + 2 ) ^{2}} + \frac{5}{( x + 2 ) ^{2}}

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

\int \frac{x ^{2}}{( x + 2 ) ^{2}} d x = x + 2 - 4 ln ∣ x + 2 ∣ - \frac{4}{x + 2}

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

= x + 2 - 4 ln ∣ x + 2 ∣ - \frac{4}{x + 2} - \frac{5}{x + 2}

Vereinfache

x + 2 - 4 ln ∣ x + 2 ∣ - \frac{4}{x + 2} - \frac{5}{x + 2} : x + 2 - 4 ln ∣ x + 2 ∣ - \frac{9}{x + 2}

= x + 2 - 4 ln ∣ x + 2 ∣ - \frac{9}{x + 2}

Füge eine Konstante zur Lösung hinzu

= x + 2 - 4 ln ∣ x + 2 ∣ - \frac{9}{x + 2} + C

Graph

Beliebte Beispiele

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

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

laplacetransform sin(2x+3)

l a pl a ce t r an s f or m sin (2 x + 3)

limit as x approaches 0 of x^3cos(5/x)

x \to 0 lim (x^{3} cos (\frac{5}{x}))

(\partial)/(\partial y)(x/(y+1))

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

fläche y=3x^2,y=2-x,x=0

a re a y = 3 x^{2}, y = 2 - x, x = 0