integral of (6x^2-4x-25)/(x-2)

Lösung

\int \frac{6 x ^{2} - 4 x - 25}{x - 2} d x

3 x^{2} + 8 x - 9 ln ∣ x - 2 ∣ - 28 + C

Schritte zur Lösung

\int \frac{6 x ^{2} - 4 x - 25}{x - 2} d x

Multipliziere aus

\frac{6 x ^{2} - 4 x - 25}{x - 2} : \frac{6 x ^{2}}{x - 2} - \frac{4 x}{x - 2} - \frac{25}{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{6 x ^{2}}{x - 2} d x - \int \frac{4 x}{x - 2} d x - \int \frac{25}{x - 2} d x

\int \frac{6 x ^{2}}{x - 2} d x = 6 (\frac{( x - 2 ) ^{2}}{2} + 4 (x - 2) + 4 ln ∣ x - 2 ∣)

\int \frac{4 x}{x - 2} d x = 4 (x - 2 + 2 ln ∣ x - 2 ∣)

\int \frac{25}{x - 2} d x = 25 ln ∣ x - 2 ∣

= 6 (\frac{( x - 2 ) ^{2}}{2} + 4 (x - 2) + 4 ln ∣ x - 2 ∣) - 4 (x - 2 + 2 ln ∣ x - 2 ∣) - 25 ln ∣ x - 2 ∣

Vereinfache

6 (\frac{( x - 2 ) ^{2}}{2} + 4 (x - 2) + 4 ln ∣ x - 2 ∣) - 4 (x - 2 + 2 ln ∣ x - 2 ∣) - 25 ln ∣ x - 2 ∣ : 3 x^{2} + 8 x - 9 ln ∣ x - 2 ∣ - 28

= 3 x^{2} + 8 x - 9 ln ∣ x - 2 ∣ - 28

Füge eine Konstante zur Lösung hinzu

= 3 x^{2} + 8 x - 9 ln ∣ x - 2 ∣ - 28 + C

h \to 0 lim (\frac{( 1 + h ) - 1}{h})

x \to - 2 lim (x^{2} - 3)

\frac{d}{d x} ([x + (x + sin^{2} (x))^{7}]^{3})

x \to 0 lim (2^{- \frac{1}{x}})

\frac{\partial}{\partial y} (y + x cos (t))