I have to show next property of stochastic integration.   Let $X$ be adapted integrand, for which we know that $E[\int_0^T X_s^2 ds] &lt; \infty$. Let $0 \leq s &lt; t \leq T $ and we have some $W \in F_s$ ($F_s$ is $\sigma$-algebra) and we know $E[\int_s^t W^2 X_s^2 ds] &lt; \infty$.  Show that $\int_s^t W X_u dBu = W \int_s^t X_u dBu$.  I think I should start first with simple integrands and then make construction on other, but I am not sure if it is obvious how to make this on simple integrands.  Thanks for help.
Let $X$ be adapted integrand, for which we know that $E[\int_0^T X_s^2 \, ds]&lt; \infty $. Let $0≤s&lt;t≤T$ and we have some $W∈F_s$ ($F_s$ is $\sigma$-algebra) and we know $E[\int_s^t W^2X_u^2 \, du]&lt;\infty$. I have to show  that $\int_s^t W X_u \, dB_u=W \int_s^t X_u dBu$.  I know that for simple integrands this follows from definition. We also know that for $X$ there exists sequence of elementary integrands $X^n$ such that $E[ \int_0^t (X^n_u-X_u)^2 \, du]$ converges to $0$, when $n \to \infty$. From this one can see that it also holds $E[ (\int_0^t (X^n_u-X_u) \, dB_u)^2]$. I wonder if I can show that it  holds $E[ |(\int_s^t W (X^n_u-X_u) \, dB_u)|] \to 0$ as $n \to \infty$ . (I think I should use Cauchy- Schwarz inequality: $E(XY)^2 \leq E(X^2)E(Y^2)$, but not sure where. If I could show this convergence in $L^1$, it would be enough for my proof. If I rewrite it as $E[E[|(\int_s^t W(X^n_u-X_u) \, dB_u)|  \mid F_s]]$ I don't know if I can put $W$ out of integral. Would it be correct? Any help would be really very appreciated. Thanks.
My try, using $x = \sec(u)$ substitution:  $$ \begin{eqnarray} \int \frac{\sqrt{x^2-1}}{x} \mathrm{d}x &amp;=&amp; \int \frac{\sqrt{\sec^2(u) - 1}}{\sec(u)}\tan(u)\sec(u) \mathrm{d}u \\ &amp;=&amp; \int \tan^2(u) \mathrm{d}u \\ &amp;=&amp; \tan(u) - u + C \\ &amp;=&amp; \tan(arcsec(x)) - arcsec(x) + C \end{eqnarray} $$  However, according to , the answer should be: $$ \int \frac{\sqrt{x^2-1}}{x} \mathrm{d}x = \sqrt{x^2-1}+\arctan \left( \frac{1}{\sqrt{x^2-1}} \right)+C $$ When I derive this last answer I don't get back the integrand, but rather: $$ \frac{\mathrm d}{\mathrm d x}\left(\sqrt{x^2-1}+\arctan \left( \frac{1}{\sqrt{x^2-1}} \right)+C\right) = \frac{x}{\sqrt{x^2-1}}- \frac{x}{(x^2-1)^{3/2}\left(1+\frac{1}{x^2-1}\right)} $$  I don't know how to simplify this expression more. Also, I am unable to check whether my answer is correct because I don't know how to find the derivative of $arcsec(x)$.  Can someone check my calculations and tell me where I've done something wrong and how one can simplify the last expression to get back the integrand? How to boot WUBI installed Ubuntu within Windows 8? I have Windows 8 Release Customer Preview on my laptop. I tried to install Ubuntu on it with Ubuntu Windows installer (I have always used this to install, although that was on Windows 7), it installs and asks to reboot, then immediately Windows 8 boots up.  I do not have the option to choose what OS to boot. How can I boot to Ubuntu? VM is not exactly what I would like to use, but it is an option, however a last resort. Any help? Verify mysqldump backup is corruption free Lazy Method for Reading Big File in Python? I have a very big file 4GB and when I try to read it my computer hangs. So I want to read it piece by piece and after processing each piece store the processed piece into another file and read next piece.  Is there any method to yield these pieces ?  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So I thought about the uncommented line: %moredelim = [is][\color{blue}\bfseries def \mdseries\color{purple}]{def\ }{(}, If I use this one and uncomment the line below I get this result:    It's nearly what I wan't but I cannot add the last, now missing ( in black color.  Does anyone has a solution for this without pretouching the code and add all the @@ symbols? Is it bad practice to return from within a try catch finally block? So I came across some code this morning that looked like this:  try {     x = SomeThingDangerous();     return x; } catch (Exception ex) {     throw new DangerousException(ex); } finally {     CleanUpDangerousStuff(); }   Now this code compiles fine and works as it should, but it just doesn't feel right to return from within a try block, especially if there's an associated finally.  My main issue is what happens if the finally throws an exception of it's own? 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