How would you Solve this Integral not using a Table

[Storm Butler]

Homework Statement

I have to figure out how to solve this integral without a table : int((2r/sqrt(r^2-s^2))*(1/2)*(R-r)^2),x,s,R) where R and s are constant parameters in the function.

Homework Equations

The Attempt at a Solution

So far i have tried breaking the function up and i got the indefinite integral down to : ∫(rR^2)/(√(r^2-S^2) ⅆr-∫(Rr^2)/√(r^2-S^2 ) ⅆr+∫r^3/√(r^2-S^2 ) ⅆr
so far i have been able to solve the integral with the R^2 term and the r^3 term (if anyone is curious on how i did this i will post my work but until then ill just leave it out) but i can't figure out how to do the middle one: ∫(Rr^2)/√(r^2-S^2 ) ⅆr without using the table i simply don't even know where to begin.

Can someone help me please, and or if you know an easier way to do the original integral it would help me a lot. thanks

 

[issacnewton]

storm, i can't understand your integral. would be nice if you can use latex or post some
pic

Newton

 

[Storm Butler]

I actually just figured out how to do it however, in the future if i post another question how do i use latex?

 

[Sourabh N]

Click on Go Advanced (just below this message box). I really wish there was an easier way to tex. (Or maybe there is and I don't know about it?)

 

[Mark44]

I actually just figured out how to do it however, in the future if i post another question how do i use latex?

Click on Go Advanced (just below this message box). I really wish there was an easier way to tex. (Or maybe there is and I don't know about it?)

https://www.physicsforums.com/showthread.php?t=386951 [Broken]

 

[Sourabh N]

Thank you!