1) Integral {(x^3)-4x}/{(x^2)+1}^2.what Is The Solution?

2) Integral {x^(1/2)}dx/{1+ X^(1/4)}.what Is The Solution?

Please help me out.i require detailed solutions.

thaking you.

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- Sep 6th 2010, 11:42 AMryanaliHelp with integration
1) Integral {(x^3)-4x}/{(x^2)+1}^2.what Is The Solution?

2) Integral {x^(1/2)}dx/{1+ X^(1/4)}.what Is The Solution?

Please help me out.i require detailed solutions.

thaking you. - Sep 6th 2010, 01:01 PMmr fantastic
- Sep 6th 2010, 01:04 PMTheCoffeeMachine
1.

Let

Then also

We have

Hence - Sep 7th 2010, 04:22 AMryanali
Thank you very much to you both for replying.I tried the first using partial fractions and substitution,but got stuck and the second one i still have no idea how to go forward.

Thank you TheCoffeeMachine.If it is is'nt too much for you could you please help me with the second one too. - Sep 7th 2010, 07:25 AMtom@ballooncalculus
Just in case a picture helps...

In fact, a choice of two - either...

http://www.ballooncalculus.org/draw/intChain/three.png

... or...

http://www.ballooncalculus.org/draw/internal/two.png

... where (key in spoiler) ...

__Spoiler__:

Either way, work anti-clockwise, and find G then F then I.

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - Sep 7th 2010, 12:40 PMmr fantastic