Thank you so much for the reply, Sir.
I changed variables from u to (u + tv - x). For which I considered P = u + vt - x, and got the following equation:
$$\int_{-\infty }^{\infty} e^{-\frac{(P+x-tv)^{2}}{4Dt}}d\sqrt{\frac{P}{tv}} \; _1F_{2}\left [ \left\{\frac{1}{2}\right\} , \left\{ 1, \frac{3}{2}\right\}, -\frac{d^{2}K^{2}P}{4vt}\right ]dp$$
Here,
$_1F_2$ is the HyperGeometricPFQ function.
Now, again I am facing the same error in integrating it in Wolfram. Please find attached the Wolfram notebook for your reference (last section).
Please do let me know if I am mistaken in incorporating your comment.
Thank you.
Attachments:
