Question

How do I evaluate `int1/sqrt(1-4x^2)dx`?

Answer 1

To evaluate the integration: `int1/sqrt(1-4x^2)`

This is very simple. You only need to recall the common integration formula using Trigonometric Substitution.

(Key step) Recall that `int1/sqrt(a^2 - u^2) = arcsin(u/a) + C`

In this case, you can observe that `a = 1` and `u = 2x` would give you the exactly format

Therefore, the answer for `int1/sqrt(1-4x^2)` is `arcsin(2x) + C` or `sin^-1(2x) + C`

Feel free to find out the formula sheet online: