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^2+2x-5)/(x-3)

Lösung

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

Lösung

\frac{( x - 3 ) ^{2}}{2} + 8 (x - 3) + 10 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u ^{2} + 8 u + 10}{u} d u

Multipliziere aus

\frac{u ^{2} + 8 u + 10}{u} : u + 8 + \frac{10}{u}

= \int u + 8 + \frac{10}{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 8 d u + \int \frac{10}{u} d u

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

\int 8 d u = 8 u

\int \frac{10}{u} d u = 10 ln ∣ u ∣

= \frac{u ^{2}}{2} + 8 u + 10 ln ∣ u ∣

Setze in

u = x - 3

ein

= \frac{( x - 3 ) ^{2}}{2} + 8 (x - 3) + 10 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{( x - 3 ) ^{2}}{2} + 8 (x - 3) + 10 ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

integral of ((x^3+3x^6))/(x^4)

\int \frac{( x ^{3} + 3 x ^{6} )}{x ^{4}} d x

integral of 7xsqrt(x^2+1)

\int 7 x x^{2} + 1 d x

integral of cos(5t)+t^4

\int cos (5 t) + t^{4} d t

integral of (1-1/x)^3*1/(x^2)

\int (1 - \frac{1}{x})^{3} \cdot \frac{1}{x ^{2}} d x

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

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