SpiralFlex
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Re: MX2 Integration Marathon
One-two line method.1) Use the substitution x=sin^2u
2)(1+2(x(1-x))^.5)^.5 then becomes (1+2cosusinu)^.5
3)We the use the fact that sin^2u+cos^2u=1 to make the above square root into sinu+cosu
4) Then the integral becomes 2sinucos^2u +2sin^2ucosu
5) this becomes (2sin^3u)/3 - (2cos^3u)/3
6) this the becomes (2(x)^1.5)/3 - (2(1-x)^1.5)/3