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#2 2005-09-13 10:42:54
- kylekatarn
- Power Member
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Re: Integration by substitution
try the substitution
z=2x²
and then integrate by parts.
I haven't solved it, but at a first glance seems a good approach.
#3 2005-09-14 16:31:22
- seiya_001
- Member
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Re: Integration by substitution
I hope this helps...
your problem is:
∫2x^2/(2x^2+1) dx
divide 2x^2/(2x^2+1) to acquire 1-(1/2x^2+1)
then: ∫ 1-(1/2x^2+1) dx = ∫dx - ∫(1/2x^2+1) dx, yay..an easier integration...!!
= x-∫(1/2x^2+1) dx, and we know that ∫1/(u^2+a^2) dx = 1/a arc tg u/a
thus: x- (arc tg x√2) or x(1-arc tg √2) + C
guys please CMIIW...
"If you can't have more age in your life, then have more life in your age..
#4 2005-09-15 01:50:39
- kylekatarn
- Power Member
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Re: Integration by substitution
Code:
√2·arctan(x√2)
x - -------------- +C
2Last edited by kylekatarn (2005-09-15 01:51:02)