>>456
　k^4 = k(k-1)(k-2)(k-3) +6k(k-1)(k-2) +7k(k-1) +k,
　Σ[k=1,n] k(k-1)(k-2)(k-3) = (n+1)n(n-1)(n-2)(n-3)/5,
　Σ[k=1,n] k(k-1)(k-2) = (n+1)n(n-1)(n-2)/4,
　Σ[k=1,n] k(k-1) = (n+1)n(n-1)/3,
　Σ[k=1,n] k = (n+1)n/2.


>>462 の補足

∫[1/x→2] y･e^(xy) dy
　= ……
　= (2/x)e^(2x) - (1/x^2)e^(2x)
　= { (1/x)e^(2x) } '.


>>481
　x^3 +1 = (x+1)(x^2 -x+1),
　1/(x^3 +1) = (1/3)/(x+1) -(1/6){(2x-1)/(x^2 -x+1)} +(1/2)/(x^2 -x+1),
I = (1/3)log|x+1| - (1/6)log(x^2 -x+1) + (1/√3)arctan((2x-1)/√3) + c.