Sqrt[1 + 4 x^2]
1/4*(2*1*sqrt(4*1^2+1)+asinh(2*1)) 1/4*(2*x*sqrt(4*x^2+1)+asinh(2*x))
Sqrt[1 + 9 x^4]
(3*(x + 9*x^5) - 2*(-1)^(1/4)*Sqrt[3 + 27*x^4]* EllipticF[I*ArcSinh[(1 + I)*Sqrt[3/2]*x], -1])/ (9*Sqrt[1 + 9*x^4])
(3*(x+9*x^5)-2*(-1)^(1/4)*sqrt(3+27*x^4)*ellipticF(sqrt(-1)*asinh((1+sqrt(-1))*sqrt(3/2)*x),-1))/(9*sqrt(1+9*x^4))
ellipticF(x,k)
Sqrt[1 + (2.1)^2 x^(2.1)]
0.48780487804878053*x*Sqrt[1. + 4.41*x^2.1] + 0.5121951219512196*x*Hypergeometric2F1[ 0.47619047619047616, 0.5, 1.4761904761904763, -4.41*x^2.1]
0.48780487804878053*x*sqrt(1. + 4.41*x^2.1) + 0.5121951219512196*x*F21( 0.47619047619047616, 0.5, 1.4761904761904763, -4.41*x^2.1)
Hypergeometric2F1[a, b, c, z] 超幾何関数 http://reference.wolfram.com/mathematica/ref/Hypergeometric2F1.html
