Note that transgalactic's proposal will enable you to find the answer by entering an integrand loop of finite length.
To see what I mean with an "integrand loop", I'll take an example:
We are to compute:
[tex]I=\int_{0}^{1}e^{x}\cos(x)dx[/tex]
we use partial integration to write this as:
[tex]I=\int_{0}^{1}e^{x}\cos(x)dx=e^{x}\cos(x)\mid^{x=1}_{x=0}+\int_{0}^{1}e^{x}\sin(x)dx=(e^{x}\cos(x)+e^{x}\sin(x))\mid_{x=0}^{x=1}-\int_{0}^{1}e^{x}\cos(x)dx=(e^{x}\cos(x)+e^{x}\sin(x))\mid_{x=0}^{x=1}-I[/tex]
Therefore, we have gained the equation for I:
[tex]I=(e^{x}\cos(x)+e^{x}\sin(x))\mid_{x=0}^{x=1}-I[/tex]
which is easily solved for I.