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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x + 2 ∣ - \frac{2}{x + 2} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 4}{x ^{2} + 4 x + 4} : \frac{x}{x ^{2} + 4 x + 4} + \frac{4}{x ^{2} + 4 x + 4}

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

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

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

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

Vereinfache

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

= ln ∣ x + 2 ∣ - \frac{2}{x + 2}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 2 ∣ - \frac{2}{x + 2} + C

Graph

Beliebte Beispiele

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

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

(dy)/(dx)=xsqrt(x-24)

\frac{d y}{d x} = x x - 24

tangent x^2+y^2=29,(2,-5)

t an g e n t x^{2} + y^{2} = 29, (2, - 5)

derivative of arcsin(sqrt(sin(x)))

\frac{d}{d x} (arcsin (sin (x)))

(df)/(dx)=tan^3(x)-sec^3(x)

\frac{df}{d x} = tan^{3} (x) - sec^{3} (x)