show the way

• Oct 14th 2009, 04:44 AM
nthethem
show the way
How does one carry out

$\int\frac{1}{(x^2+1)^2}dx$
• Oct 14th 2009, 04:52 AM
tom@ballooncalculus
- Wolfram|Alpha

Click on 'show steps'

Edit:

Just in case a picture helps...

http://www.ballooncalculus.org/asy/t...ernal/aTan.png

... where

http://www.ballooncalculus.org/asy/chain.png

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which subject to the chain rule).

Carry on the anti-clockwise journey (to I) by finding G(theta) and mapping back from tan(theta) to x.

__________________________________________

Don't integrate - balloontegrate!

http://www.ballooncalculus.org/examples/gallery.html

http://www.ballooncalculus.org/asy/doc.html
• Oct 14th 2009, 05:47 AM
HallsofIvy
Quote:

Originally Posted by nthethem
How does one carry out

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

What Tom@ballooncalculus is saying, in his own unique way, is that, since $tan^2(u)+ 1= set^2(u)$, use the substitution tan(u)= x.