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samer_guirguis_2000 x^2=sin(y) is a good substitution
dx=1/2 cos(y)/sin^.5(y) dy Mr F remarks: $\displaystyle {\color{red}dx = \frac{1}{2} \frac{\cos y}{x}}$ is sufficient - there's no need to express x in terms of y.
sqrt(1-x^4)=cos(y)
you will be integrating 1/2 cos^2(y) dy