Solving Gaussian Integral: Stuck on Step

[smallgirl]

Hey,

I am rather stuck on this gaussian integral...

I have come this far, and not sure what to do now:

\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+\frac{\Delta k^{2}(t-x)^{2}h_{01}}{2}-ik_{0}(t-x)h_{01}[\tex]<br /> <br /> \int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}})&lt;br /&gt; [\tex]&lt;br /&gt; &lt;br /&gt; \int dh_{01}(-((\frac{h_{01}}{\sigma}-\frac{\sigma}{2}k_{0}(t-x)\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}}))[\tex]&amp;lt;br /&amp;gt; &amp;lt;br /&amp;gt; \int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}}))^{2})-\frac{\sigma^{2}}{4}(t-x)^{2}k_{0}^{2}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}})^{2}[\tex]&amp;amp;lt;br /&amp;amp;gt; &amp;amp;lt;br /&amp;amp;gt; where a=-1 b=1/2&amp;amp;lt;br /&amp;amp;gt; &amp;amp;lt;br /&amp;amp;gt; Not sure what to do now...

 

[mathman]

Hey,

I am rather stuck on this gaussian integral...

I have come this far, and not sure what to do now:

\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+\frac{\Delta k^{2}(t-x)^{2}h_{01}}{2}-ik_{0}(t-x)h_{01}

\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}})<br />

\int dh_{01}(-((\frac{h_{01}}{\sigma}-\frac{\sigma}{2}k_{0}(t-x)\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}}))

\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}}))^{2})-\frac{\sigma^{2}}{4}(t-x)^{2}k_{0}^{2}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}})^{2}

where a=-1 b=1/2

Not sure what to do now...

You need to change \tex to /tex. Even so, the equations look weird. It is not at all clear what you are doing.