# [✓] Calculate a double integration of two functions?

GROUPS:
 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 :)
27 days ago
5 Replies
 HelloFirst 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 MariuszPS: Next time post code not image.SEE
27 days ago
 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.
 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] *)