Realize that your series expansion is only valid in the range -1<=x<=1.

Also, for your proof to be complete, you should include an arbitrary constant c when you integrate to get line 2. By substituting x=0 you can determine that c=0.

the series converges very slowly so for getting 5- 6 decimal point precision you would need 400 terms

Realize that your series expansion is only valid in the range -1<=x<=1.

Also, for your proof to be complete, you should include an arbitrary constant c when you integrate to get line 2. By substituting x=0 you can determine that c=0.

the series converges very slowly so for getting 5- 6 decimal point precision you would need 400 terms