de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (2-x)/(sqrt(9-4x^2))

Lösung

\int \frac{2 - x}{9 - 4 x ^{2}} d x

Lösung

arcsin (\frac{2}{3} x) + \frac{1}{4} 9 - 4 x^{2} + C

Schritte zur Lösung

\int \frac{2 - x}{9 - 4 x ^{2}} d x

Multipliziere aus

\frac{2 - x}{9 - 4 x ^{2}} : \frac{2}{9 - 4 x ^{2}} - \frac{x}{9 - 4 x ^{2}}

= \int \frac{2}{9 - 4 x ^{2}} - \frac{x}{9 - 4 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{2}{9 - 4 x ^{2}} d x - \int \frac{x}{9 - 4 x ^{2}} d x

\int \frac{2}{9 - 4 x ^{2}} d x = arcsin (\frac{2}{3} x)

\int \frac{x}{9 - 4 x ^{2}} d x = - \frac{1}{4} 9 - 4 x^{2}

= arcsin (\frac{2}{3} x) - (- \frac{1}{4} 9 - 4 x^{2})

Vereinfache

= arcsin (\frac{2}{3} x) + \frac{1}{4} 9 - 4 x^{2}

Füge eine Konstante zur Lösung hinzu

= arcsin (\frac{2}{3} x) + \frac{1}{4} 9 - 4 x^{2} + C

Graph

Beliebte Beispiele

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

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

integral of 8e^{4x}-1

\int 8 e^{4 x} - 1 d x

integral of 2x^3ln(4x)

\int 2 x^{3} ln (4 x) d x

integral of 3t\sqrt[3]{2t^2-11}

\int 3 t 3 2 t^{2} - 11 d t

integral of e^x+1/(5x)

\int e^{x} + \frac{1}{5 x} d x