de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (6x^2-32x+41)/(x-4)

Lösung

\int \frac{6 x ^{2} - 32 x + 41}{x - 4} d x

Lösung

3 x^{2} - 8 x + 9 ln ∣ x - 4 ∣ - 16 + C

Schritte zur Lösung

\int \frac{6 x ^{2} - 32 x + 41}{x - 4} d x

Multipliziere aus

\frac{6 x ^{2} - 32 x + 41}{x - 4} : \frac{6 x ^{2}}{x - 4} - \frac{32 x}{x - 4} + \frac{41}{x - 4}

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 - 4} d x - \int \frac{32 x}{x - 4} d x + \int \frac{41}{x - 4} d x

\int \frac{6 x ^{2}}{x - 4} d x = 6 (\frac{( x - 4 ) ^{2}}{2} + 8 (x - 4) + 16 ln ∣ x - 4 ∣)

\int \frac{32 x}{x - 4} d x = 32 (x - 4 + 4 ln ∣ x - 4 ∣)

\int \frac{41}{x - 4} d x = 41 ln ∣ x - 4 ∣

= 6 (\frac{( x - 4 ) ^{2}}{2} + 8 (x - 4) + 16 ln ∣ x - 4 ∣) - 32 (x - 4 + 4 ln ∣ x - 4 ∣) + 41 ln ∣ x - 4 ∣

Vereinfache

6 (\frac{( x - 4 ) ^{2}}{2} + 8 (x - 4) + 16 ln ∣ x - 4 ∣) - 32 (x - 4 + 4 ln ∣ x - 4 ∣) + 41 ln ∣ x - 4 ∣ : 3 x^{2} - 8 x + 9 ln ∣ x - 4 ∣ - 16

= 3 x^{2} - 8 x + 9 ln ∣ x - 4 ∣ - 16

Füge eine Konstante zur Lösung hinzu

= 3 x^{2} - 8 x + 9 ln ∣ x - 4 ∣ - 16 + C

Graph

Beliebte Beispiele

integral of (x^3)/((x^2-4)^{3/2)}

\int \frac{x ^{3}}{( x ^{2} - 4 ) ^{\frac{3}{2}}} d x

integral of x/(sqrt((x^2-25)^3))

\int \frac{x}{( x ^{2} - 25 ) ^{3}} d x

integral of log_{6}(x-1)

\int lo g_{6} (x - 1) d x

integral of (xe^x)/((x+1))

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

integral of sqrt(x^2-4x-45)

\int x^{2} - 4 x - 45 d x