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Beliebt Rechnen >

integral of 3/(x(x+1))

Lösung

\int \frac{3}{x ( x + 1 )} d x

Lösung

3 (ln ∣ x ∣ - ln ∣ x + 1 ∣) + C

Schritte zur Lösung

\int \frac{3}{x ( x + 1 )} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{1}{x ( x + 1 )} d x

Ermittle den Partialbruch von

\frac{1}{x ( x + 1 )} : \frac{1}{x} - \frac{1}{x + 1}

= 3 \cdot \int \frac{1}{x} - \frac{1}{x + 1} 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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= 3 (ln ∣ x ∣ - ln ∣ x + 1 ∣)

Füge eine Konstante zur Lösung hinzu

= 3 (ln ∣ x ∣ - ln ∣ x + 1 ∣) + C

Graph

Beliebte Beispiele

integral of ((x^3-1))/(x(x+1)^2)

\int \frac{( x ^{3} - 1 )}{x ( x + 1 ) ^{2}} d x

integral of (3/x-(10)/(x^6))

\int (\frac{3}{x} - \frac{10}{x ^{6}}) d x

derivative of 1/((2x+1^3))

\frac{d}{d x} (\frac{1}{( 2 x + 1 ) ^{3}})

integral of 1+t

\int 1 + t d t

derivative of ((x+30sqrt(x^2+100))/x)

\frac{d}{d x} (\frac{( x + 30 ) x ^{2} + 100}{x})