# How to find this integral $I=\int_{0}^{1} t^{-1/2}\left(1-\frac{t}{1+4y}\right)^{-1/2-ix}dt$

Question:

Find the closed form of

$$I(x,y)=\int_{0}^{1}t^{-1/2}\left(1-\dfrac{t}{1+4y}\right)^{-1/2-ix}dt$$

where $i^2=-1$

I have used Wolfram Alpha but it can't help me out. How to find it?

Thank you

I have explained why I can't comment, because in China we can't comment in MSE, (I don't know why?) Now, I can only post questions and I also can answer questions , but I can't comment.

china math110 also said that he can't comment. Here is the proof: How find all positive real $\beta$ such A finite number of $\left|\frac{p}{q}-\sqrt{2}\right|<\frac{\beta}{q^2}$

How prove $f(a_{i})=0$ if $\int_{0}^{1}x^kf(x)dx=0,k=1,2,3,\cdots,n$

• Mr. @CameronWilliams, I can understand if he doesn't wanna interact with those that comment and answer china math's problem. Don't be so harsh about that ツ – Anastasiya-Romanova 秀 Oct 5 '14 at 15:47
• wolf can't help - Yeah... wolves never do... :-( – Lucian Oct 5 '14 at 15:52