integral of (1+sqrt(9-x^2))

Lösung

\int (1 + 9 - x^{2}) d x

x + \frac{9}{2} (arcsin (\frac{1}{3} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{3} x))) + C

Schritte zur Lösung

\int 1 + 9 - 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 1 d x + \int 9 - x^{2} d x

\int 1 d x = x

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

= x + \frac{9}{2} (arcsin (\frac{1}{3} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{3} x)))

Füge eine Konstante zur Lösung hinzu

= x + \frac{9}{2} (arcsin (\frac{1}{3} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{3} x))) + C

\frac{d}{d x} (4 x^{3} - 6 x)

l a pl a ce t r an s f or m 3 - e^{2 t}

d er i v a t i v e f (x) = \frac{5 x + 1}{x - 1}

a re a y = x^{2} - 4, y = 8 - 2 x^{2}

\frac{\partial}{\partial y} (- 3 e^{x} cos (yz))