## 1039 Reputation

4 years, 307 days

## @vv  I copy code,paste,execute,dos...

I copy code,paste,execute,dosen't work?

If I convert to 1D  then works.

I'm confused.

## .....

On Maple 2018.1 yours attached file works fine.Maple calculate  all worksheet about 30 seconds.

See result:

 >
 >
 >
 (1)
 >

 >
 >
 >
 >
 >
 >
 >
 (2)
 >
 (3)
 >

If you have problem then  try this worksheet below:

aquestion_(1)_ver2.mw

## ....

For general integral with general constans :

`int(lambda[1]*alpha^2*exp(lambda[1]*Z)/((exp(lambda[1]*Z)-1+alpha)^2*(exp(lambda[2]*Z)-1+alpha)), Z = 0 .. infinity)`

Maple 2018.1 can't find symbolic solution.

```r[1] := proc (lambda1, lambda2, alpha) options operator, arrow; lambda1*alpha^2*exp(lambda1*Z)/((exp(lambda1*Z)-1+alpha)^2*(exp(lambda2*Z)-1+alpha)) end proc;
R[1] := int(eval(diff(r[1](lambda1, lambda2, alpha), lambda1), [lambda1 = 3/10, lambda2 = 2*(1/10), alpha = 4]), Z = 0 .. infinity, numeric);

#R[1] := 1.077997357```

aquestion_(1).mw

## Only comment....

I gave you only a comment,my point of view. Wait for the answer.

And so at the end you'll end up with numerical calculations.

## ....

You have a Transcendental equations that why Maple can't solve(Any CAS can't solve).Transcendental equations have no analytical solution.

Try numeric solver like fsolve, DirectSearch package,or something else.

## ....

I updated my answer.Its the same answer like done by  the user Carl Love.Probably a better simplification can not be done.

Ei_ver2.mw

## Workaround....

restart;

assume(R::real, z::real); is(-R+sqrt(R^2+z^2) < 0);

#false

## Use assuming....

`assuming`([convert(signum(0, R-sqrt(R^2+z^2), 1), piecewise)], [R-sqrt(R^2+z^2) < 0]);

# -1

or:

`assuming`([signum(0, R-sqrt(R^2+z^2), 1)], [R-sqrt(R^2+z^2) < 0])

#-1

Maple have some limitation about regarding the resolution of the case and falsehood.

restart:

assume(R > 0, z > 0, R in real, z in real);

coulditbe(R-sqrt(R^2+z^2) < 0);#FAIL

is(R-sqrt(R^2+z^2) < 0);#FAIL

## From Wikipedia......

From Wikipedia, using property: Ei(1,z) = - Ei(-z) and faster converging series by Ramanujan:

For example, for z = 10,and for  40 terms  an answer correct to 16 significant figures.

series.mw

## Check....

A numeric check gives a big numbers in domain x=(-5,5) and z=(-5,5).Integral is divergent.

```r := 2.5;
Q := proc (x, z) options operator, arrow; evalf(Int(1/(x*r^2*cos(x-y)+z*r^2*sin(z-y))^5, y = 0 .. Pi, method = _Gquad, epsilon = 1/100000)) end proc;
seq(seq(lprint(Q(x, z)), x = -5 .. 5, .25), z = -5 .. 5, .25);
```

-0.3091653839e55
0.7846201518e57
0.2353821795e58
-0.7841865263e57
-0.7756899663e57
0.1123370081e58
...

## ....

@ssllys You are welcome :)

## ....

@mmcdara . Thanks for checking :)

## Works on Maple 2017.3 and 2018....

All  my code in answer works on Maple 2017.3 and 2018. I don't have earlier version of Maple, so I will not check it.

## ....

I edited the answer.It should work now.

All code was exectuted in Maple 2018.

 First 10 11 12 13 14 15 16 Last Page 12 of 25
﻿