de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (7x^3+3x)/(x-1)

Lösung

\int \frac{7 x ^{3} + 3 x}{x - 1} d x

Lösung

24 x + 10 ln ∣ x - 1 ∣ + \frac{7}{3} (x - 1)^{3} + \frac{21}{2} (x - 1)^{2} - 24 + C

Schritte zur Lösung

\int \frac{7 x ^{3} + 3 x}{x - 1} d x

Multipliziere aus

\frac{7 x ^{3} + 3 x}{x - 1} : \frac{7 x ^{3}}{x - 1} + \frac{3 x}{x - 1}

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

\int \frac{7 x ^{3}}{x - 1} d x = 7 (\frac{( x - 1 ) ^{3}}{3} + \frac{3 ( x - 1 ) ^{2}}{2} + 3 (x - 1) + ln ∣ x - 1 ∣)

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

= 7 (\frac{( x - 1 ) ^{3}}{3} + \frac{3 ( x - 1 ) ^{2}}{2} + 3 (x - 1) + ln ∣ x - 1 ∣) + 3 (x - 1 + ln ∣ x - 1 ∣)

Vereinfache

7 (\frac{( x - 1 ) ^{3}}{3} + \frac{3 ( x - 1 ) ^{2}}{2} + 3 (x - 1) + ln ∣ x - 1 ∣) + 3 (x - 1 + ln ∣ x - 1 ∣) : 24 x + 10 ln ∣ x - 1 ∣ + \frac{7}{3} (x - 1)^{3} + \frac{21}{2} (x - 1)^{2} - 24

= 24 x + 10 ln ∣ x - 1 ∣ + \frac{7}{3} (x - 1)^{3} + \frac{21}{2} (x - 1)^{2} - 24

Füge eine Konstante zur Lösung hinzu

= 24 x + 10 ln ∣ x - 1 ∣ + \frac{7}{3} (x - 1)^{3} + \frac{21}{2} (x - 1)^{2} - 24 + C

Graph

Beliebte Beispiele

integral of 3e^{-2x}

\int 3 e^{- 2 x} d x

derivative (2x^4)/(cos(x)e^x)

d er i v a t i v e \frac{2 x ^{4}}{cos ( x ) e ^{x}}

limit as x approaches 3+of (|x-3|)/(x-3)

x \to 3 + lim (\frac{∣ x - 3 ∣}{x - 3})

integral of 1/(1-sin(x))

\int \frac{1}{1 - sin ( x )} d x

limit as x approaches 0 of (sin(2)(x))/x

x \to 0 lim (\frac{sin ( 2 ) ( x )}{x})