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#1 2005-09-13 00:33:51

Archon
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Integration by substitution

hey im in college level calc and i am wondering if you could help me with this problem

∫2x^2/(2x^2+1) dx

thx for all your help

#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
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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
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Re: Integration by substitution

Code:

    √2·arctan(x√2) 
x - -------------- +C
             2

Last edited by kylekatarn (2005-09-15 01:51:02)

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