Hi, all!
So basically I’m trying to do a double integration of two functions but in one case Mathematica outputs “Null” in the answer while in the other case it outputs the same input and doesn’t really do anything.
Here below are snapshots of code and the output given by Mathematica.
Thanks in advance 
Hello
First integral can’t be solved symbolically. Integral with gamma function has no antiderivative with standard elementary function or maybe known special function, no discovery yet. Use NIntegrate,a numericall integrator.
NIntegrate[Gamma[n + 1]/Gamma[k + 1]*1/Gamma[n - k + 1]*(1/10000)^k, {n, 25, 500}, {k, 2, 25}]
(* 0.0481051 *)
Second integral, you did little mistake in syntax.
Integrate[(x*y^2)*(1/(x^2 + 1)), {x, 0, 1}, {y, -3, 3}]
(* Log[512] *)
Regards Mariusz
PS: Next time post code not image. SEE
Please make sure you know the rules: https://wolfr.am/READ-1ST
Do NOT post code as images.
Dear Mariusz Iwaniuk,
Thank you so much for your response. It was a great help
However, for the second part where you mentioned removing the comma, I get a different answer when I do the same thing by hand. When I do it manually, I get the answer as “9 ln 2” instead of “Log [512]”
I realise that 9 ln 2 = ln 512, but aren’t Log and Ln different?
Sorry for the confusion, I’m a complete beginner to Mathematica.
Thank you so much,
Raivat S.
Oops, sorry I’m a complete beginner. I will make sure that this doesn’t happen again.
In Mathematica Log[z] gives the natural logarithm of z (logarithm to base e) and
Log[b,z] gives the logarithm to base b.
Log[512]//PowerExpand
(* 9 Log[2] *)