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.
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 cant figure out how to do the middle one: ∫(Rr^2)/√(r^2-S^2 ) ⅆr without using the table i simply dont 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