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Trig Substitution for Integration question?
∫ [x√(x^2 + 1)] dx
When I try to solve this problem, I get as far as 4 ∫ (tan theta)(sec theta)^3 d theta. Assuming I have done it right so far, where do I go from here?
I made a mistake in typing the question. It is x^2 + 4 inside the root, not x^2 + 1.
2 Answers
- Anonymous1 decade agoFavorite Answer
when you get to the point (tan theta)(sec theta)^3, separate it into (tan theta)(sec theta) * (sec theta)^2 d theta. Then do a u sub and make u = sec theta. I have the whole problem written out I'm trying to scan it so you can see it all written out. But that should help you finish if you know what you're doing.
*edit*
Here's the work written out.
http://img301.imageshack.us/img301/8068/sc00089ab1...
Written out with +4 instead doesn't change much.
- 1 decade ago
Just let u =x^2+1,
du=2x
1/2 integral u^.5
2/6 * (x^2+1)^1.5 +c
Same Method, the deriv is the same because the deriv of 4 and 1 is zero.
