MapleSAcomp.mws

>    Int(2*Pi*(x+1)*sqrt(1+9*x^4),x=0..2);

Int(2*Pi*(x+1)*(1+9*x^4)^(1/2),x = 0 .. 2)

>    value(%);

10/3*Pi*145^(1/2)+1/6*Pi*ln(12+145^(1/2))+4/9*Pi*3^(1/2)*EllipticK(1/2*2^(1/2))-2/9*Pi*3^(1/2)*EllipticF(4/13*3^(1/2),1/2*2^(1/2))

>    evalf(%);

131.5504597

>    Int(2*Pi*(x+1)*sqrt(1+9*x^4),x=0..2);

Int(2*Pi*(x+1)*(1+9*x^4)^(1/2),x = 0 .. 2)

>    evalf(%);

131.5504597

>    Int(2*Pi*(1+y^(1/3))*sqrt(1+(1/9)*y^(-4/3)),y=0..8);

Int(2/3*Pi*(1+y^(1/3))*(9+1/(y^(4/3)))^(1/2),y = 0 .. 8)

>    value(%);

(1/576-1/576*I)*Pi*((72*8^(1/3)+1)*8^(2/3))^(1/2)*8^(2/3)*(1728*6^(1/2)+4*8^(1/3)*6^(1/2)+291*8^(2/3)*6^(1/2)+291*I*8^(2/3)*6^(1/2)+1728*I*6^(1/2)+4*I*8^(1/3)*6^(1/2)+16*(1-3*I*8^(2/3))^(1/2)*(1+3*I*8^...
(1/576-1/576*I)*Pi*((72*8^(1/3)+1)*8^(2/3))^(1/2)*8^(2/3)*(1728*6^(1/2)+4*8^(1/3)*6^(1/2)+291*8^(2/3)*6^(1/2)+291*I*8^(2/3)*6^(1/2)+1728*I*6^(1/2)+4*I*8^(1/3)*6^(1/2)+16*(1-3*I*8^(2/3))^(1/2)*(1+3*I*8^...
(1/576-1/576*I)*Pi*((72*8^(1/3)+1)*8^(2/3))^(1/2)*8^(2/3)*(1728*6^(1/2)+4*8^(1/3)*6^(1/2)+291*8^(2/3)*6^(1/2)+291*I*8^(2/3)*6^(1/2)+1728*I*6^(1/2)+4*I*8^(1/3)*6^(1/2)+16*(1-3*I*8^(2/3))^(1/2)*(1+3*I*8^...

>    evalf(%);

131.5504597+0.*I

>    Int(2*Pi*(1+y^(1/3))*sqrt(1+(1/9)*y^(-4/3)),y=0..8);

Int(2/3*Pi*(1+y^(1/3))*(9+1/(y^(4/3)))^(1/2),y = 0 .. 8)

>    evalf(%);

131.5504597

>