I have the following integration that I want to evaluate it using Mathematica.

```
Evaluate(Sqrt((Theta))/(Sqrt(p ) BesselK(1, Sqrt(p (Theta))))
Integrate(
x BesselK(0,
x Sqrt(p (Theta))) (Sqrt((Theta))/Sqrt(
s ) (rTD BesselK(1,
rTD Sqrt(s (Theta))) (BesselI(0, x Sqrt(s (Theta))) -
BesselK(0, x Sqrt(s (Theta))) BesselI(0, Sqrt(
s (Theta)))/BesselK(0, Sqrt(s (Theta))))
+
BesselI(0,
x Sqrt(s (Theta))) (x BesselK(1, x Sqrt(s (Theta))) -
rTD BesselK(1, rTD Sqrt(s (Theta)))) HeavisideTheta(
x - rTD)
+
BesselK(0,
x Sqrt(s (Theta))) (x BesselI(1, x Sqrt(s (Theta))) -
rTD BesselI(1, rTD Sqrt(s (Theta)))) HeavisideTheta(
x - rTD))), {x, 1, Infinity}))
```

I find problem in obtaining the solution using Mathematica, so I tried to evaluate it manually.

I want to make sure that my solution is correct. My solution is as follows.