integral of (x-2)sqrt(8-x)

Lösung

\int (x - 2) 8 - x d x

\frac{2}{5} (8 - x)^{\frac{5}{2}} - 4 (8 - x)^{\frac{3}{2}} + C

Schritte zur Lösung

\int (x - 2) 8 - x d x

Multipliziere aus

(x - 2) 8 - x : x 8 - x - 2 8 - x

= \int x 8 - x - 2 8 - 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 x 8 - x d x - \int 2 8 - x d x

\int x 8 - x d x = \frac{2}{5} (8 - x)^{\frac{5}{2}} - \frac{16}{3} (8 - x)^{\frac{3}{2}}

\int 2 8 - x d x = - \frac{4}{3} (8 - x)^{\frac{3}{2}}

= \frac{2}{5} (8 - x)^{\frac{5}{2}} - \frac{16}{3} (8 - x)^{\frac{3}{2}} - (- \frac{4}{3} (8 - x)^{\frac{3}{2}})

Vereinfache

\frac{2}{5} (8 - x)^{\frac{5}{2}} - \frac{16}{3} (8 - x)^{\frac{3}{2}} - (- \frac{4}{3} (8 - x)^{\frac{3}{2}}) : \frac{2}{5} (8 - x)^{\frac{5}{2}} - 4 (8 - x)^{\frac{3}{2}}

= \frac{2}{5} (8 - x)^{\frac{5}{2}} - 4 (8 - x)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} (8 - x)^{\frac{5}{2}} - 4 (8 - x)^{\frac{3}{2}} + C

d er i v a t i v e 9 - t

n = 0 \sum \infty \frac{4}{5 ^{n - 1}}

x \to - 2 - lim (\frac{x}{x + 2})

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

x \to 64 lim (x^{\frac{2}{3}})