Question

\[\int {\frac{{dx}}{{\sqrt {x(x - 4)} }}} \]

My result is arcsin((x+2)/2)


Can you please verify ?

Answer 1

derivative of sin^-1 ((x+2)/2)
= -sqrt(-x (x+4))/(x (x+4))
= 1/sqrt(-x(x+4))
so i don't think it's the correct answer, sorry
in latex (clearer)
\[\large \frac{1}{\sqrt(-x(x+4))}\]

Answer 2

that being said, the longhand of doing the integral of 1/sqrt x(x-4) is something @Directrix is awesome at, and it's pretty late here, sooo...... ?

Answer 3

@Christos are you here?

Answer 4

yes @ash2326

Answer 5

How did you solve the problem?

Answer 6

well

Answer 7

I multiplied the denominator parts

Answer 8

then I add 4 - 4

Answer 9

if I do that then I can get -(x +2)^2 + 4

Answer 10

in other words 2^2 - (x + 2)^2 in the denominator

Answer 11

and thats arcsin

Answer 12

are you sure arcsin x? I think its (1-x^2) in the square root

Answer 13

I meant that integral of
\[\int\frac{1}{\sqrt{1-x^2}} dx=\sin^{-1} x\]

Answer 14

@Christos ???