Question

Use a change of variables to find the following indefinite integrals.
\[
\int\frac{1}{\sqrt{1-9x^{2}}}\; dx
\]

Answer 1

try 3x = sin(u)

so 3dx = cos(u)du

so we get int(du/3)

= u/3 + C

= arcsin(3x)/3 + C

Answer 2

That is impressive, how did you came up with u?

Answer 3

if you don't really need to understand the method here, you can find this form of equation and its solution in an integral table.

Answer 4

it's impressive to you...but i have done problems like this many times from experience.

i came up with u because i knew that you can always integrate something of the form 1/sqrt(1 - u^2)...it's just arcsin(u)

so i transformed the integral into something like that with a substitution

Answer 5

@jamesm, ah, that makes sense, it's kinda frustrating that they put this kind of exercise at the beginning of integral learning :(. Thanks for your help, I really appreciate it.