integral of 1/(sqrt((x-9)(3-x)))

Lösung

\int \frac{1}{( x - 9 ) ( 3 - x )} d x

arcsin (\frac{1}{3} (x - 6)) + C

Schritte zur Lösung

\int \frac{1}{( x - 9 ) ( 3 - x )} d x

\frac{1}{( x - 9 ) ( 3 - x )} = \frac{1 - ( x - 9 ) ( 3 - x )}{( x - 9 ) ( 3 - x )} + 1

= \int \frac{1 - ( x - 9 ) ( 3 - x )}{( x - 9 ) ( 3 - x )} + 1 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{1 - ( x - 9 ) ( 3 - x )}{( x - 9 ) ( 3 - x )} d x + \int 1 d x

\int \frac{1 - ( x - 9 ) ( 3 - x )}{( x - 9 ) ( 3 - x )} d x = arcsin (\frac{1}{3} (x - 6)) - x

\int 1 d x = x

= arcsin (\frac{1}{3} (x - 6)) - x + x

Vereinfache

= arcsin (\frac{1}{3} (x - 6))

Füge eine Konstante zur Lösung hinzu

= arcsin (\frac{1}{3} (x - 6)) + C

x y^{^{''}} + 2 y^{^{'}} = 24 x^{2}

\int - 5 x d x

d er i v a t i v e y = (3 x^{2} + 2) (4 x - 1)

\frac{d}{d x} (\frac{e ^{x}}{x ^{2}})

y^{^{''}} + 4 y = e - t