Integrate Lim -a to +a underroot a-x / a +x

Question

Integration 

Answer 1

It would be a LOT easier if that square root wasn't there!

Answer 2

You can find integral but it diverges. 

∫(a-x)/(a+x)dx=∫(2a/(a+x)-1)dx=(2aln(a+x)-x)|_-a^a=

=2a[ln(2a)-1- lim_ε→0(ln(a+ε-a)]=2aln(2ae)-(-∞)=∞.

Answer 3

Divide  a-x / a+x

 

           =   -1 +  (2a)/(a+x)

 

 

Integrating with respect to x:

 

    -x + (2a) ln | a + x|

 

As x--> +a    ,    the integral converges to   -a + (2a) ln | 2a |

 

But as x--> -a, the integral diverges -a + (2a) ln|0|