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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x + 1 ∣ + \frac{4}{x + 2} + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x ^{2}}{( x + 1 ) ( x + 2 ) ^{2}} : \frac{1}{x + 1} - \frac{4}{( x + 2 ) ^{2}}

= \int \frac{1}{x + 1} - \frac{4}{( x + 2 ) ^{2}} d x

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}{x + 1} d x - \int \frac{4}{( x + 2 ) ^{2}} d x

\int \frac{1}{x + 1} d x = ln ∣ x + 1 ∣

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

= ln ∣ x + 1 ∣ - (- \frac{4}{x + 2})

Vereinfache

= ln ∣ x + 1 ∣ + \frac{4}{x + 2}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 1 ∣ + \frac{4}{x + 2} + C

Graph

Beliebte Beispiele

integral of x^2e^{xy}

\int x^{2} e^{x y} d y

integral of e^{(-x)/3}

\int e^{\frac{- x}{3}} d x

integral from-2 to 3 of (27)/(x^4)

\int_{- 2}^{3} \frac{27}{x ^{4}} d x

xy^2y^'=y^3-1x^3

x y^{2} y^{^{'}} = y^{3} - 1 x^{3}

(\partial)/(\partial y)((-x)/((x+y)^2))

\frac{\partial}{\partial y} (\frac{- x}{( x + y ) ^{2}})