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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 3}{x ( x + 2 )} : \frac{x}{x ( x + 2 )} + \frac{3}{x ( x + 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}{x ( x + 2 )} d x + \int \frac{3}{x ( x + 2 )} d x

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

\int \frac{3}{x ( x + 2 )} d x = 3 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 2 ∣)

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

Vereinfache

ln ∣ x + 2 ∣ + 3 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 2 ∣) : \frac{3}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x + 2 ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (x+2)/(sqrt(x^2+6x+36))

\int \frac{x + 2}{x ^{2} + 6 x + 36} d x

integral of (-1)/(x(ln(x))^4)

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

integral of (4^{ln(1/x)})/x

\int \frac{4 ^{l n (\frac{1}{x})}}{x} d x

integral of (-3)/(x(ln(x))^3)

\int \frac{- 3}{x ( ln ( x ) ) ^{3}} d x

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

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