/ 2\ |/ ___\ | ||1 - \/ x | | acos||---------| | || ___| | \\1 + \/ x / /
acos(((1 - sqrt(x))/(1 + sqrt(x)))^2)
/ ___ \ / ___\ | 1 1 - \/ x | -\1 - \/ x /*|- ----------------- - ------------------| | ___ / ___\ 2| | \/ x *\1 + \/ x / ___ / ___\ | \ \/ x *\1 + \/ x / / -------------------------------------------------------- __________________ / 4 / / ___\ / ___\ / \1 - \/ x / \1 + \/ x /* / 1 - ------------ / 4 / / ___\ \/ \1 + \/ x /
/ ___ / ___\\ 2 ___ / ___\ | 1 2 -1 + \/ x 2*\-1 + \/ x /| / ___\ 4 / ___\ -1 + \/ x \-1 + \/ x /*|- ---- - ------------- + ---------------- + --------------| / ___\ | -1 + \/ x | / ___\ | -1 + \/ x | -1 + ---------- | 3/2 / ___\ 3/2 / ___\ 2| \-1 + \/ x /*|-1 + ----------| \-1 + \/ x / *|-1 + ----------| ___ | x x*\1 + \/ x / x *\1 + \/ x / / ___\ | | ___ | | ___ | 1 + \/ x \ x*\1 + \/ x / / \ 1 + \/ x / \ 1 + \/ x / --------------- - ------------------------------------------------------------------------- - ------------------------------ - --------------------------------- 2*x 2 / ___\ / 4\ 2*x*\1 + \/ x / 4 | / ___\ | / ___\ | \1 - \/ x / | x*\1 + \/ x / *|1 - ------------| | 4| | / ___\ | \ \1 + \/ x / / ---------------------------------------------------------------------------------------------------------------------------------------------------------------- __________________ / 4 2 / / ___\ / ___\ / \1 - \/ x / \1 + \/ x / * / 1 - ------------ / 4 / / ___\ \/ \1 + \/ x /
/ 2 2\ ___ / ___\ / ___ / ___\ / ___\ \ / ___ / ___\\ 2 2 3 4 / ___\ / ___ / ___\\ 3 / ___\ | ___ / ___\ / ___\ / ___\ | 1 2 -1 + \/ x 2*\-1 + \/ x / ___ / ___\ | 1 2 2 -1 + \/ x 2*\-1 + \/ x / 2*\-1 + \/ x / | ___ / ___\ / ___\ | 1 2 -1 + \/ x 2*\-1 + \/ x /| / ___\ 4 / ___\ 3 / ___\ 7 / ___\ / ___\ | -1 + \/ x | | 1 2 -1 + \/ x 2*\-1 + \/ x /| / ___\ | -1 + \/ x | |3 -1 + \/ x \-1 + \/ x / 8*\-1 + \/ x / 5*\-1 + \/ x / | - ---- - ------------- + ---------------- + -------------- -1 + \/ x 3*\-1 + \/ x /*|- ---- - -------------- - ----------------- + ---------------- + --------------- + -----------------| -1 + \/ x / ___\ | -1 + \/ x | \-1 + \/ x /*|- ---- - ------------- + ---------------- + --------------| / ___\ | -1 + \/ x | / ___\ | -1 + \/ x | / ___\ | -1 + \/ x | / ___\ | -1 + \/ x | \-1 + \/ x / *|-1 + ----------|*|- ---- - ------------- + ---------------- + --------------| \-1 + \/ x / *|-1 + ----------|*|- - ---------- + ---------------- - -------------- + ---------------| 3/2 / ___\ 3/2 / ___\ 2 -1 + ---------- | 5/2 2 / ___\ 2 5/2 / ___\ 2 3| -1 + ---------- \-1 + \/ x /*|-1 + ----------| | 3/2 / ___\ 3/2 / ___\ 2| \-1 + \/ x /*|-1 + ----------| \-1 + \/ x / *|-1 + ----------| \-1 + \/ x / *|-1 + ----------| 3*\-1 + \/ x / *|-1 + ----------| | ___ | | 3/2 / ___\ 3/2 / ___\ 2| | ___ | |x 3/2 3/2 / ___\ / ___\ 2| x x*\1 + \/ x / x *\1 + \/ x / / ___\ ___ | x x *\1 + \/ x / 3/2 / ___\ x *\1 + \/ x / 2 / ___\ 3/2 / ___\ | ___ | ___ | | x x*\1 + \/ x / x *\1 + \/ x / / ___\ | | ___ | | ___ | | ___ | | ___ | \ 1 + \/ x / | x x*\1 + \/ x / x *\1 + \/ x / / ___\ | \ 1 + \/ x / | x x *\1 + \/ x / x*\1 + \/ x / / ___\ | x*\1 + \/ x / 1 + \/ x \ x *\1 + \/ x / x *\1 + \/ x / x *\1 + \/ x / / 1 + \/ x \ 1 + \/ x / \ x*\1 + \/ x / / \ 1 + \/ x / \ 1 + \/ x / \ 1 + \/ x / \ 1 + \/ x / \ x*\1 + \/ x / / \ x*\1 + \/ x / / - ---------------------------------------------------------- - --------------- + --------------------------------------------------------------------------------------------------------------------- - ------------------ + ------------------------------ + ------------------------------------------------------------------------- + ------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------- + -------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------ ___ 2 4 3/2 / ___\ 2 ___ / ___\ 2 / ___\ / 4\ / 4\ 2 / 4\ / 4\ 2*\/ x 4*x 2*x *\1 + \/ x / 3/2 / ___\ 2*\/ x *\1 + \/ x / 4*x *\1 + \/ x / 5 | / ___\ | 4 | / ___\ | / 4\ 4 | / ___\ | 4 | / ___\ | 2*x *\1 + \/ x / 3/2 / ___\ | \1 - \/ x / | 3/2 / ___\ | \1 - \/ x / | 8 | / ___\ | ___ / ___\ | \1 - \/ x / | ___ / ___\ | \1 - \/ x / | x *\1 + \/ x / *|1 - ------------| x *\1 + \/ x / *|1 - ------------| 3/2 / ___\ | \1 - \/ x / | \/ x *\1 + \/ x / *|1 - ------------| 2*\/ x *\1 + \/ x / *|1 - ------------| | 4| | 4| x *\1 + \/ x / *|1 - ------------| | 4| | 4| | / ___\ | | / ___\ | | 4| | / ___\ | | / ___\ | \ \1 + \/ x / / \ \1 + \/ x / / | / ___\ | \ \1 + \/ x / / \ \1 + \/ x / / \ \1 + \/ x / / ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- __________________ / 4 2 / / ___\ / ___\ / \1 - \/ x / \1 + \/ x / * / 1 - ------------ / 4 / / ___\ \/ \1 + \/ x /