Helpppp!

[jonlarr31]

Complex Integration Help

How do you integrate (sinx)/(1+x^2)dx from -1 to 1? I know that the answer is zero, but I can't figure out how to show all of the steps. At first glance, the problem seems easy, but arctangent is involved and it get's very tricky, very fast. A friend said that I should redefine sin(x), but I don't know what to change it to. Please help! Even a link to a website that shows how to solve the problem would be greatly appreciated.

 

[Deleted member 4993]

How do you integrate (sinx)/(1+x^2)dx from -1 to 1? I know that the answer is zero, but I can't figure out how to show all of the steps. At first glance, the problem seems easy, but arctangent is involved and it get's very tricky, very fast. A friend said that I should redefine sin(x), but I don't know what to change it to. Please help! Even a link to a website that shows how to solve the problem would be greatly appreciated.

Yes it is a very nasty "non-elementary" integral - check it out at Wolfram-Alfa.

If I were asked to solve the problem - I would claim that (sinx)/(1+x^2) is an odd-function hence integral (-a) to (+a) is always zero.