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Beliebt Rechnen >

integral of 1/((x+3)(x+4))

Lösung

\int \frac{1}{( x + 3 ) ( x + 4 )} d x

Lösung

ln ∣ x + 3 ∣ - ln ∣ x + 4 ∣ + C

Schritte zur Lösung

\int \frac{1}{( x + 3 ) ( x + 4 )} d x

Ermittle den Partialbruch von

\frac{1}{( x + 3 ) ( x + 4 )} : \frac{1}{x + 3} - \frac{1}{x + 4}

= \int \frac{1}{x + 3} - \frac{1}{x + 4} 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 + 3} d x - \int \frac{1}{x + 4} d x

\int \frac{1}{x + 3} d x = ln ∣ x + 3 ∣

\int \frac{1}{x + 4} d x = ln ∣ x + 4 ∣

= ln ∣ x + 3 ∣ - ln ∣ x + 4 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 3 ∣ - ln ∣ x + 4 ∣ + C

Graph

Beliebte Beispiele

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

in t e g r a l (x^{2} + 3) (x - 1)

integral of (5^{3ln(x)})/x

\int \frac{5 ^{3 l n (x)}}{x} d x

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

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

integral of-20 1/((1+2x)^2)

\int - 20 \frac{1}{( 1 + 2 x ) ^{2}} d x

integral of e^{-3u}

\int e^{- 3 u} d u