Math Problem Solver

"f(x) = ∫[0,∞] (Σ[n=1 to 1000] ((x^n)/n!) * e^(-x)) dx + lim[t→∞] { Σ[k=1 to t] [ (1/k) * cos(πk/2) ] } + Π[n=1 to 500] (1 + (1/n)^2) + log(e^(x^2 + 2x + 1) / √(2π)) + { tan⁻¹(Σ[m=1 to 100] [(x^m)/(m^2)]) / √(x+1) }^2 + (d/dx)[x^3 * ln(x) - e^(-x)] * [Σ[k=1 to 100](k^2)] + ∬[0,1] x^2 + y^2 dxdy - ∑[i=1 to ∞] [((-1)^i)/(2i+1)]π + Γ(x)*ζ(3) + (∂²/∂x²)[cos(x)*sin(x)]!"