[SOLVED] integration

**ronaldo_07** · January 9th 2009, 12:18 PM

$\int \frac{-4x}{4x^4+4x^2+1}$

$\int \frac{-4x}{(2x^2+1)(2x^2+1)}$

What would my next steps be to complete this integral?

**red_dog** · January 9th 2009, 12:28 PM

Use the substitution $2x^2+1=t\Rightarrow 4xdx=dt$

**ronaldo_07** · January 9th 2009, 01:07 PM

$\int\frac{-4x}{t^2}*\frac{dt}{4x}$

$\int\frac{1}{(2x^2+1)(2x^2+1)}$

is this correct?

**tom@ballooncalculus** · January 9th 2009, 01:12 PM

And, if a picture helps...

Straight continuous lines differentiate/integrate with respect to x, the straight dashed line with respect to the dashed balloon expression - as though it were a variable like u.

Don't integrate - balloontegrate! Balloon Calculus: worked examples from past papers

**ronaldo_07** · January 9th 2009, 02:50 PM

As my answer I got $y=\frac{1}{2x^2+1}+C$

**tom@ballooncalculus** · January 9th 2009, 03:28 PM

Yep

**ronaldo_07** · January 9th 2009, 04:50 PM

thanks

**mr fantastic** · January 9th 2009, 06:36 PM

Originally Posted by ronaldo_07

As my answer I got $y=\frac{1}{2x^2+1}+C$

You can always differentiate it and see if you get back the integrand.

**tom@ballooncalculus** · January 10th 2009, 01:23 AM

Yes - and of course the differentiation is the same picture (completed) but read downwards instead of up.

Don't integrate - balloontegrate! http://www.ballooncalculus.org/examples.png

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