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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of pi(x^3-1)^2-(x-1)^2

\int π (x^{3} - 1)^{2} - (x - 1)^{2} d x

integral of-1/5

\int - \frac{1}{5} d x

integral of xtan(x)sec^3(x)

\int x tan (x) sec^{3} (x) d x

integral of t/(2-t)

\int \frac{t}{2 - t} d t

integral of (sqrt(1-x^4))/(x^5)

\int \frac{1 - x ^{4}}{x ^{5}} d x