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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{( x + 1 ) ^{2}}{2} - 5 (x + 1) + 6 ln ∣ x + 1 ∣ + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u ^{2} - 5 u + 6}{u} d u

Multipliziere aus

\frac{u ^{2} - 5 u + 6}{u} : u - 5 + \frac{6}{u}

= \int u - 5 + \frac{6}{u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u - \int 5 d u + \int \frac{6}{u} d u

\int u d u = \frac{u ^{2}}{2}

\int 5 d u = 5 u

\int \frac{6}{u} d u = 6 ln ∣ u ∣

= \frac{u ^{2}}{2} - 5 u + 6 ln ∣ u ∣

Setze in

u = x + 1

ein

= \frac{( x + 1 ) ^{2}}{2} - 5 (x + 1) + 6 ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{( x + 1 ) ^{2}}{2} - 5 (x + 1) + 6 ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

integral of-7/((x^2+7)^{3/2)}

\int - \frac{7}{( x ^{2} + 7 ) ^{\frac{3}{2}}} d x

integral of ((x^4))/((x-1)^2(x+2))

\int \frac{( x ^{4} )}{( x - 1 ) ^{2} ( x + 2 )} d x

integral of 3x^2(2-x^3)^8

\int 3 x^{2} (2 - x^{3})^{8} d x

integral of (e^x)/((e^x-6)(e^x+1))

\int \frac{e ^{x}}{( e ^{x} - 6 ) ( e ^{x} + 1 )} d x

integral of (ln(x^2))/(3x)

\int \frac{ln ( x ^{2} )}{3 x} d x