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-1)/(sqrt(9-x^2))

Lösung

\int \frac{x - 1}{9 - x ^{2}} d x

Lösung

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

Schritte zur Lösung

\int \frac{x - 1}{9 - x ^{2}} d x

Multipliziere aus

\frac{x - 1}{9 - x ^{2}} : \frac{x}{9 - x ^{2}} - \frac{1}{9 - x ^{2}}

= \int \frac{x}{9 - x ^{2}} - \frac{1}{9 - 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}{9 - x ^{2}} d x - \int \frac{1}{9 - x ^{2}} d x

\int \frac{x}{9 - x ^{2}} d x = - 9 - x^{2}

\int \frac{1}{9 - x ^{2}} d x = arcsin (\frac{1}{3} x)

= - 9 - x^{2} - arcsin (\frac{1}{3} x)

Füge eine Konstante zur Lösung hinzu

= - 9 - x^{2} - arcsin (\frac{1}{3} x) + C

Graph

Beliebte Beispiele

integral of (x^4-6x^2+3)/(x^4)

\int \frac{x ^{4} - 6 x ^{2} + 3}{x ^{4}} d x

integral of sin(y^3)y^2

\int sin (y^{3}) y^{2} d y

integral of (x-e^x)

\int (x - e^{x}) d x

integral of 12x^2e^{2x^3}

\int 12 x^{2} e^{2 x^{3}} d x

integral of 4sqrt(x)e^{sqrt(x)}

\int 4 x e^{x} d x