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(81-4x^2))

Lösung

\int \frac{( x - 1 )}{81 - 4 x ^{2}} d x

Lösung

- \frac{1}{4} 81 - 4 x^{2} - \frac{1}{2} arcsin (\frac{2}{9} x) + C

Schritte zur Lösung

\int \frac{x - 1}{81 - 4 x ^{2}} d x

Multipliziere aus

\frac{x - 1}{81 - 4 x ^{2}} : \frac{x}{81 - 4 x ^{2}} - \frac{1}{81 - 4 x ^{2}}

= \int \frac{x}{81 - 4 x ^{2}} - \frac{1}{81 - 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{x}{81 - 4 x ^{2}} d x - \int \frac{1}{81 - 4 x ^{2}} d x

\int \frac{x}{81 - 4 x ^{2}} d x = - \frac{1}{4} 81 - 4 x^{2}

\int \frac{1}{81 - 4 x ^{2}} d x = \frac{1}{2} arcsin (\frac{2}{9} x)

= - \frac{1}{4} 81 - 4 x^{2} - \frac{1}{2} arcsin (\frac{2}{9} x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} 81 - 4 x^{2} - \frac{1}{2} arcsin (\frac{2}{9} x) + C

Graph

Beliebte Beispiele

integral of 1/(1+9cos(x))

\int \frac{1}{1 + 9 cos ( x )} d x

integral of (5x-2)/(x(-2))

\int \frac{5 x - 2}{x ( - 2 )} d x

integral of (5x^2)/((x-3)^3)

\int \frac{5 x ^{2}}{( x - 3 ) ^{3}} d x

integral of (6x^2-11x+7)/(3x-1)

\int \frac{6 x ^{2} - 11 x + 7}{3 x - 1} d x

integral of (1x-2)/(sqrt(x)+4)

\int \frac{1 x - 2}{x + 4} d x