de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (a-x)sqrt(a+x)

Lösung

\int (a - x) a + x d x

Lösung

\frac{4}{3} a (x + a)^{\frac{3}{2}} - \frac{2}{5} (x + a)^{\frac{5}{2}} + C

Schritte zur Lösung

\int (a - x) a + x d x

Multipliziere aus

(a - x) a + x : a a + x - x a + x

= \int a a + x - x a + x 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 a a + x d x - \int x a + x d x

\int a a + x d x = a \frac{2}{3} (a + x)^{\frac{3}{2}}

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

= a \frac{2}{3} (a + x)^{\frac{3}{2}} - (\frac{2}{5} (a + x)^{\frac{5}{2}} - a \frac{2}{3} (a + x)^{\frac{3}{2}})

Vereinfache

a \frac{2}{3} (a + x)^{\frac{3}{2}} - (\frac{2}{5} (a + x)^{\frac{5}{2}} - a \frac{2}{3} (a + x)^{\frac{3}{2}}) : \frac{4}{3} a (x + a)^{\frac{3}{2}} - \frac{2}{5} (x + a)^{\frac{5}{2}}

= \frac{4}{3} a (x + a)^{\frac{3}{2}} - \frac{2}{5} (x + a)^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} a (x + a)^{\frac{3}{2}} - \frac{2}{5} (x + a)^{\frac{5}{2}} + C

Graph

Beliebte Beispiele

integral of e^{3x}+5e^{-x}

\int e^{3 x} + 5 e^{- x} d x

integral of (ln(1-x))

\int (ln (1 - x)) d x

integral of (cos^4(x))/(csc^3(x))

\int \frac{cos ^{4} ( x )}{csc ^{3} ( x )} d x

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

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

integral of-sin(3x)(5+cos(3x))^4

\int - sin (3 x) (5 + cos (3 x))^{4} d x