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)/(x-10)

Lösung

\int \frac{x ^{2}}{x - 10} d x

Lösung

\frac{( x - 10 ) ^{2}}{2} + 20 (x - 10) + 100 ln ∣ x - 10 ∣ + C

Schritte zur Lösung

\int \frac{x ^{2}}{x - 10} d x

Wende U-Substitution an

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

Multipliziere aus

\frac{( u + 10 ) ^{2}}{u} : u + 20 + \frac{100}{u}

= \int u + 20 + \frac{100}{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 20 d u + \int \frac{100}{u} d u

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

\int 20 d u = 20 u

\int \frac{100}{u} d u = 100 ln ∣ u ∣

= \frac{u ^{2}}{2} + 20 u + 100 ln ∣ u ∣

Setze in

u = x - 10

ein

= \frac{( x - 10 ) ^{2}}{2} + 20 (x - 10) + 100 ln ∣ x - 10 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{( x - 10 ) ^{2}}{2} + 20 (x - 10) + 100 ln ∣ x - 10 ∣ + C

Graph

Beliebte Beispiele

(dy)/(dx)=(4x+y)^2

\frac{d y}{d x} = (4 x + y)^{2}

derivative of (x^3-1/(x-1))

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

(\partial)/(\partial x)(ln(10x))

\frac{\partial}{\partial x} (ln (10 x))

derivative of x/(log_{e(x)})

\frac{d}{d x} (\frac{x}{lo g _{e} ( x )})

derivative of be^{-x}

\frac{d}{d x} (b e^{- x})