# Thread: integration by mathematica

1. ## integration by mathematica

Hi Guys,

I need to solve the following integral using mathematica, but i do not know how to identify the constants and do symbolic integration, so i get a very nasty expression .

dw/dt=(t-r)/{(t-b)*(t-p)*sqrt((t-a)*(t-c))}

a,b ,p,c,r are constants.

any help with this!

Thanks

mopen80

2. ## Re: integration by mathematica

I'm not sure about the Mathematica expressions, but I'm pretty sure you can solve this using partial fractions (it won't be pretty though)...

3. ## Re: integration by mathematica

Originally Posted by mopen80
Hi Guys,

I need to solve the following integral using mathematica, but i do not know how to identify the constants and do symbolic integration, so i get a very nasty expression .

dw/dt=(t-r)/{(t-b)*(t-p)*sqrt((t-a)*(t-c))}

a,b ,p,c,r are constants.

any help with this!

Thanks

mopen80
$$\frac{dw}{dt}=\frac{t-r}{(t-b)(t-p)\sqrt{(t-a)(t-c)}}$$

The output from Mathematica is

$$\int \frac{t-r}{(t-b) (t-p) \sqrt{(t-a) (t-c)}} \, dt=$$

$$\frac{\sqrt{t-a} \sqrt{t-c} \left(i \sqrt{a-p} (b-r) \sqrt{c-p} \log \left(\frac{i (b-p) \left(a (b-2 c+t)+2 i \sqrt{a-b} \sqrt{t-a} \sqrt{b-c} \sqrt{t-c}+b (c-2 t)+c t\right)}{\sqrt{a-b} \sqrt{b-c} (b-r) (b-t)}\right)+\sqrt{a-b} \sqrt{b-c} (p-r) \log (p-t)+\sqrt{a-b} \sqrt{b-c} (r-p) \log \left(-a (-2 c+p+t)+2 \left(\sqrt{a-p} \sqrt{t-a} \sqrt{c-p} \sqrt{t-c}+p t\right)-c (p+t)\right)\right)}{\sqrt{a-b} \sqrt{a-p} \sqrt{b-c} (p-b) \sqrt{c-p} \sqrt{(t-a) (t-c)}}$$

That is what it is. I don't know how you can simplify it without having values for your constants.

4. ## Re: integration by mathematica

Thanks

I got this expression already in Mathematica.Any guidelines to solve this using partial fraction then?

Thanks