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int(x/((1-4x^2)^1/2)) is equal to?
int(x/((1-4x^2)^1/2)) = 1/4 arcsin(2x) + c
The books says the answer is -1/4(1-4x^2)^1/2 + c is the solution. Yeah, I know that this is surely correct, and easier than the way I used, but I was wondering whether my answer is also true or if I did something wrong somewhere.
My substitution is:
u = 2x, since 1/rt(1-u^2) = arcsin(u). Am I mistaken!
I did ask this question before, but I forgot to add the substitution, and it was becoming old. If I added it at that time, probably the question wasn't going to be answered any further.
2 Answers
- Anonymous1 decade agoFavorite Answer
You have forgotten the x in the numerator so your method is invalid. Your answer would have been correct if the original integral had been 1/(1 - 4x^2)^(1/2)
Didn't you ask this question before. It was answered there.
- 1 decade ago
I've confirmed the book's answer, but I'm still not sure as to how you've solved the problem.
