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**Archon****Member**- Registered: 2005-09-12
- Posts: 1

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

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

try the substitution**z=2x²**

and then integrate by parts.

I haven't solved it, but at a first glance seems a good approach.

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**seiya_001****Member**- Registered: 2005-08-23
- Posts: 19

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..**

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

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

*Last edited by kylekatarn (2005-09-14 03:51:02)*

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