de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x^4-5x^2+3x-4)/(x+1)

Lösung

\int \frac{x ^{4} - 5 x ^{2} + 3 x - 4}{x + 1} d x

Lösung

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 12 x - 11 ln ∣ x + 1 ∣ - \frac{5}{2} (x + 1)^{2} + 13 + C

Schritte zur Lösung

\int \frac{x ^{4} - 5 x ^{2} + 3 x - 4}{x + 1} d x

Multipliziere aus

\frac{x ^{4} - 5 x ^{2} + 3 x - 4}{x + 1} : \frac{x ^{4}}{x + 1} - \frac{5 x ^{2}}{x + 1} + \frac{3 x}{x + 1} - \frac{4}{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{x ^{4}}{x + 1} d x - \int \frac{5 x ^{2}}{x + 1} d x + \int \frac{3 x}{x + 1} d x - \int \frac{4}{x + 1} d x

\int \frac{x ^{4}}{x + 1} d x = \frac{x ^{4}}{4} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x + ln ∣ x + 1 ∣

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

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

\int \frac{4}{x + 1} d x = 4 ln ∣ x + 1 ∣

= \frac{x ^{4}}{4} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x + ln ∣ x + 1 ∣ - 5 (\frac{( x + 1 ) ^{2}}{2} - 2 (x + 1) + ln ∣ x + 1 ∣) + 3 (x + 1 - ln ∣ x + 1 ∣) - 4 ln ∣ x + 1 ∣

Vereinfache

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x + ln ∣ x + 1 ∣ - 5 (\frac{( x + 1 ) ^{2}}{2} - 2 (x + 1) + ln ∣ x + 1 ∣) + 3 (x + 1 - ln ∣ x + 1 ∣) - 4 ln ∣ x + 1 ∣ : \frac{x ^{4}}{4} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 12 x - 11 ln ∣ x + 1 ∣ - \frac{5}{2} (x + 1)^{2} + 13

= \frac{x ^{4}}{4} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 12 x - 11 ln ∣ x + 1 ∣ - \frac{5}{2} (x + 1)^{2} + 13

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 12 x - 11 ln ∣ x + 1 ∣ - \frac{5}{2} (x + 1)^{2} + 13 + C

Graph

Beliebte Beispiele

integral of sqrt(3-y)

\int 3 - y d y

integral of (sqrt(x)-\sqrt[3]{x})

\int (x - 3 x) d x

integral of 26x

\int 26 x d x

integral of (2x)/((x+2)(x+3))

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

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

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