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Beliebt Rechnen >

integral of (x^2+4x-7)/(x-1)

Lösung

\int \frac{x ^{2} + 4 x - 7}{x - 1} d x

Lösung

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

Schritte zur Lösung

\int \frac{x ^{2} + 4 x - 7}{x - 1} d x

Wende U-Substitution an

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

Multipliziere aus

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

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

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

\int 6 d u = 6 u

\int \frac{2}{u} d u = 2 ln ∣ u ∣

= \frac{u ^{2}}{2} + 6 u - 2 ln ∣ u ∣

Setze in

u = x - 1

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of (8x-1/(6x+7))

\frac{d}{d x} (\frac{8 x - 1}{6 x + 7})

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

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

integral from-2 to 4 of |t^2-2t-3|

\int_{- 2}^{4} t^{2} - 2 t - 3 d t

f^'(x)=2x^2+3x-2

f^{^{'}} (x) = 2 x^{2} + 3 x - 2

(\partial)/(\partial x)(x^4y-x^2y^3)

\frac{\partial}{\partial x} (x^{4} y - x^{2} y^{3})