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^3)/(x^2-25)

Lösung

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

Lösung

\frac{1}{2} (x^{2} - 25 + 25 ln x^{2} - 25) + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u + 25}{2 u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{u + 25}{u} d u

Multipliziere aus

\frac{u + 25}{u} : 1 + \frac{25}{u}

= \frac{1}{2} \cdot \int 1 + \frac{25}{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

= \frac{1}{2} (\int 1 d u + \int \frac{25}{u} d u)

\int 1 d u = u

\int \frac{25}{u} d u = 25 ln ∣ u ∣

= \frac{1}{2} (u + 25 ln ∣ u ∣)

Setze in

u = x^{2} - 25

ein

= \frac{1}{2} (x^{2} - 25 + 25 ln x^{2} - 25)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (x^{2} - 25 + 25 ln x^{2} - 25) + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(sqrt(x^2-2x+3))

derivative of (4x/3)

fläche 8/(1+x^4),4x^2

y^'+y/t =3cos(2t)

(dy)/(dx)=(y+x)/(y-x)