# Solving intergration equation

I am trying to determine $\gamma$ such that $$\int_0^T\exp\left(\frac{3t(T-t/2)\gamma\sigma}{T^2}+\alpha t+\frac{\sigma^2}{2}\left[t-\frac{3t^2}{T^3}\left(T-\frac{t}{2}\right)^2\right]\right)\;dt=K,$$ for some constants $T$, $\sigma$, $\alpha$ and $K$. I think it can be solved analytically in terms of error function but I dont know how. I have tried bisection method using a trapezoidal method to numerically integrate but it fails.

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 Just to be sure, the problem is given $T,\sigma,\alpha,K$, find $\gamma$ such the equation holds, is it? – matgaio May 15 '12 at 21:13 @matgaio, yes that's right. – Vaolter May 16 '12 at 8:55