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Beliebt Rechnen >

integral of (x+4)/(x^3+x^2-2)

Lösung

\int \frac{x + 4}{x ^{3} + x ^{2} - 2} d x

Lösung

ln ∣ x - 1 ∣ - \frac{1}{2} ln x^{2} + 2 x + 2 - arctan (x + 1) + C

Schritte zur Lösung

\int \frac{x + 4}{x ^{3} + x ^{2} - 2} d x

Ermittle den Partialbruch von

\frac{x + 4}{x ^{3} + x ^{2} - 2} : \frac{1}{x - 1} + \frac{- x - 2}{x ^{2} + 2 x + 2}

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

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

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

= ln ∣ x - 1 ∣ - \frac{1}{2} ln x^{2} + 2 x + 2 - arctan (x + 1)

Füge eine Konstante zur Lösung hinzu

= ln ∣ x - 1 ∣ - \frac{1}{2} ln x^{2} + 2 x + 2 - arctan (x + 1) + C

Graph

Beliebte Beispiele

d/(d{y)}({x}^{{y}^{{z}}})

\frac{d}{d y} (x^{y^{z}})

derivative f(x)= 5/(1-9x)

d er i v a t i v e f (x) = \frac{5}{1 - 9 x}

derivative f(x)=6e^x+4x^2

d er i v a t i v e f (x) = 6 e^{x} + 4 x^{2}

(\partial)/(\partial y)(cos(12x)sin(3y))

\frac{\partial}{\partial y} (cos (12 x) sin (3 y))

integral of 1/(sqrt(9-y^2))

\int \frac{1}{9 - y ^{2}} d y