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))/(sqrt(3-x^2))

Lösung

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

Lösung

\frac{3}{2} (arcsin (\frac{1}{3} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{3} x))) + 3 - x^{2} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{2} - x}{3 - x ^{2}} : \frac{x ^{2}}{3 - x ^{2}} - \frac{x}{3 - x ^{2}}

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

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

\int \frac{x ^{2}}{3 - x ^{2}} d x = \frac{3}{2} (arcsin (\frac{1}{3} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{3} x)))

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

= \frac{3}{2} (arcsin (\frac{1}{3} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{3} x))) - (- 3 - x^{2})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} (arcsin (\frac{1}{3} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{3} x))) + 3 - x^{2} + C

Graph

Beliebte Beispiele

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

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

integral of sec(x)tan(x)sqrt(3+sec(x))

\int sec (x) tan (x) 3 + sec (x) d x

integral of sqrt(x)(x^2+3x-8)

\int x (x^{2} + 3 x - 8) d x

integral of 1/(x^8+x)

\int \frac{1}{x ^{8} + x} d x

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

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