de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

6 (\frac{1}{5} (1 - x)^{\frac{5}{2}} - \frac{2}{3} (1 - x)^{\frac{3}{2}} + 1 - x) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= - 3 \cdot \int - 2 (- u^{2} + 1)^{2} d u

Entferne die Konstante:

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

= - 3 (- 2 \cdot \int (- u^{2} + 1)^{2} d u)

Multipliziere aus

(- u^{2} + 1)^{2} : u^{4} - 2 u^{2} + 1

= - 3 (- 2 \cdot \int u^{4} - 2 u^{2} + 1 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

= - 3 (- 2 (\int u^{4} d u - \int 2 u^{2} d u + \int 1 d u))

\int u^{4} d u = \frac{u ^{5}}{5}

\int 2 u^{2} d u = \frac{2 u ^{3}}{3}

\int 1 d u = u

= - 3 (- 2 (\frac{u ^{5}}{5} - \frac{2 u ^{3}}{3} + u))

Setze in

u = 1 - x

ein

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

Vereinfache

- 3 (- 2 (\frac{( 1 - x ) ^{5}}{5} - \frac{2 ( 1 - x ) ^{3}}{3} + 1 - x)) : 6 (\frac{1}{5} (1 - x)^{\frac{5}{2}} - \frac{2}{3} (1 - x)^{\frac{3}{2}} + 1 - x)

= 6 (\frac{1}{5} (1 - x)^{\frac{5}{2}} - \frac{2}{3} (1 - x)^{\frac{3}{2}} + 1 - x)

Füge eine Konstante zur Lösung hinzu

= 6 (\frac{1}{5} (1 - x)^{\frac{5}{2}} - \frac{2}{3} (1 - x)^{\frac{3}{2}} + 1 - x) + C

Graph

Beliebte Beispiele

integral of 8ln(x^2-1)

\int 8 ln (x^{2} - 1) d x

f(x)= 1/(xln(x))

f (x) = \frac{1}{x ln ( x )}

integral from 0 to 1 of sqrt(64t^2+9t^4)

\int_{0}^{1} 64 t^{2} + 9 t^{4} d t

derivative tan(sqrt(3t))

d er i v a t i v e tan (3 t)

integral of 2tsqrt(2t-3)

\int 2 t 2 t - 3 d t