________ / 2 \/ 1 - x / | | _____________ | / 2 2 | \/ 3 - x - y dx | / ________ / 2 -\/ 1 - x
Integral(sqrt(3 - x^2 - y^2), (x, -sqrt(1 - x^2), sqrt(1 - x^2)))
// _________________________ _________________________ \ || _________________________ _________________________ / 2 / 2 | || / 2 / 2 / x / 2\ / x \ 2 / x / 2\ / x \ | || / x / 2\ 2 / x / 2\ 6*I* / -1 + ------------------ *\3 - y /*acosh|-----------------------| 2*I*y * / -1 + ------------------ *\3 - y /*acosh|-----------------------| | || 3*pi* / -1 + ------------------ *\3 - y / ____________________ ____________________ pi*y * / -1 + ------------------ *\3 - y / ____________________ / / 2\ | ____________________| / / 2\ | ____________________| | || / / 2\ 3 / / 2\ / / 2\ / / 2\ 2 / / 2\ \/ polar_lift\3 - y / | / / 2\ | \/ polar_lift\3 - y / | / / 2\ | | 2 | | || \/ polar_lift\3 - y / 2*I*x *\/ polar_lift\3 - y / 6*I*x*\/ polar_lift\3 - y / \/ polar_lift\3 - y / 2*I*x*y *\/ polar_lift\3 - y / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | x | | ||- --------------------------------------------------------------------------- - --------------------------------------------------------------------------- + --------------------------------------------------------------------------- + --------------------------------------------------------------------------- - --------------------------------------------------------------------------- + --------------------------------------------------------------------------- - ------------------------------------------------------------------------------ for |-------| > 1| || _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ | 2| | || / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 |-3 + y | | / || / x 2 / x / x 2 / x / x 2 / x / x 2 / x / x 2 / x / x 2 / x / x 2 / x | | || - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | | _____________ || / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ | | / 2 2 || \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / | | \/ 3 - x - y dx = C + |< | | || ________________________ ________________________ | / || / 2 / 2 | || / x / 2\ / x \ 2 / x / 2\ / x \ | || 3* / 1 - ------------------ *\3 - y /*asin|-----------------------| y * / 1 - ------------------ *\3 - y /*asin|-----------------------| | || ____________________ ____________________ ____________________ / / 2\ | ____________________| / / 2\ | ____________________| | || 3 / / 2\ / / 2\ 2 / / 2\ \/ polar_lift\3 - y / | / / 2\ | \/ polar_lift\3 - y / | / / 2\ | | || x *\/ polar_lift\3 - y / 3*x*\/ polar_lift\3 - y / x*y *\/ polar_lift\3 - y / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | || ------------------------------------------------------------------------ - ------------------------------------------------------------------------ + ------------------------------------------------------------------------ - ------------------------------------------------------------------------ + ------------------------------------------------------------------------ otherwise | || ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ | || / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 | || / x 2 / x / x 2 / x / x 2 / x / x 2 / x / x 2 / x | || - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | || / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ | \\ \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / /
/ ________ | / 2 | \/ 1 - x | / | | | | / _________________________ _________________________ _________________________ _________________________ | | | / 2 / 2 \ ____________________ / 2 \ ____________________ / 2 \ / 2 / 2 \ ____________________ / 2 \ / 2 / 2 \ / 2 / 2 \ | | | / x / 2\ | 12*x 4*x*y | 3 / / 2\ | 12*x 4*x*y | / / 2\ | 12*x 4*x*y | 2 / x / 2\ | 12*x 4*x*y | 2 / / 2\ | 12*x 4*x*y | / x / 2\ | 12*x 4*x*y | / x \ 2 / x / 2\ | 12*x 4*x*y | / x \ | | | 3*pi* / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------| 2*I*x *\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| 6*I*x*\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| pi*y * / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------| 2*I*x*y *\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| 6*I* / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------|*acosh|-----------------------| 2*I*y * / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------|*acosh|-----------------------| | | | / / 2\ | _________________________ _________________________ | | _________________________ _________________________ | | _________________________ _________________________ | / / 2\ | _________________________ _________________________ | | _________________________ _________________________ | / / 2\ | _________________________ _________________________ | | ____________________| / / 2\ | _________________________ _________________________ | | ____________________| | | | \/ polar_lift\3 - y / | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | / 2\ / x \ 2 / 2\ / x \ | | | | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / 6*I*x*\3 - y /*acosh|-----------------------| 2*I*x*y *\3 - y /*acosh|-----------------------| | | | ____________________ ____________________ ____________________ | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | ____________________| | ____________________| | | | / / 2\ 2 / / 2\ 2 / / 2\ / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ | | / / 2\ | | 2 | | | | 6*I*\/ polar_lift\3 - y / 6*I*x *\/ polar_lift\3 - y / 2*I*y *\/ polar_lift\3 - y / 6*I*\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / 2*I*y *\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / 3*pi*x*\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / pi*x*y *\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | x | | | |--------------------------------------------------------------------------- - --------------------------------------------------------------------------- - --------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------- for |-------| > 1 | | | _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ / _________________________ _________________________\ 2 2 / _________________________ _________________________\ 2 2 _________________________ / _________________________ _________________________\ 2 2 _________________________ / _________________________ _________________________\ 2 _________________________ / _________________________ _________________________\ _________________________ / _________________________ _________________________\ | 2| | | | / 2 / 2 / 2 / 2 / 2 / 2 | / 2 / 2 | ____________________ / _________________________ _________________________\ / _________________________ _________________________\ | / 2 / 2 | ____________________ / _________________________ _________________________\ / _________________________ _________________________\ / 2 | / 2 / 2 | / _________________________ _________________________\ / _________________________ _________________________\ / 2 | / 2 / 2 | / _________________________ _________________________\ / 2 | / 2 / 2 | / 2 | / 2 / 2 | |-3 + y | | | | / x 2 / x / x 2 / x / x 2 / x | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ | / 2 / 2 | / x | / x 2 / x | / 2\ / x | / x 2 / x | / 2\ | | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | / x 2 / x | | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | | | / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | / / 2\ | / / 2\ / / 2\ | | | | \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / ________ ________ | | | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / / 2 / 2 | | < dx for \/ 1 - x > -\/ 1 - x | | | ________________________ ________________________ | | | ____________________ / 2 \ ____________________ / 2 \ ____________________ / 2 \ / 2 / 2 \ / 2 / 2 \ | | | 3 / / 2\ | 6*x 2*x*y | / / 2\ | 6*x 2*x*y | 2 / / 2\ | 6*x 2*x*y | / x / 2\ | 6*x 2*x*y | / x \ 2 / x / 2\ | 6*x 2*x*y | / x \ | | | x *\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| 3*x*\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| x*y *\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| 3* / 1 - ------------------ *\3 - y /*|- ------------------------------------------------- + -------------------------------------------------|*asin|-----------------------| y * / 1 - ------------------ *\3 - y /*|- ------------------------------------------------- + -------------------------------------------------|*asin|-----------------------| | | | | ________________________ ________________________ | | ________________________ ________________________ | | ________________________ ________________________ | / / 2\ | ________________________ ________________________ | | ____________________| / / 2\ | ________________________ ________________________ | | ____________________| | | | | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | / 2\ / x \ 2 / 2\ / x \ | | | | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / 3*x*\3 - y /*asin|-----------------------| x*y *\3 - y /*asin|-----------------------| | | | ____________________ ____________________ ____________________ | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | ____________________| | ____________________| | | | / / 2\ 2 / / 2\ / 2\ 2 / / 2\ | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ | | / / 2\ | | | | 3*\/ polar_lift\3 - y / y *\/ polar_lift\3 - y / 3*\3 - y / 3*x *\/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / y *\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | | | - ------------------------------------------------------------------------ + ------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- otherwise | | | ________________________ ________________________ ________________________ ________________________ / ________________________ ________________________\ ________________________ ________________________ 2 / ________________________ ________________________\ 2 2 2 2 ________________________ / ________________________ ________________________\ ________________________ / ________________________ ________________________\ | | | / 2 / 2 / 2 / 2 | / 2 / 2 | ____________________ / 2 / 2 / ________________________ ________________________\ | / 2 / 2 | ____________________ / ________________________ ________________________\ / ________________________ ________________________\ / ________________________ ________________________\ / ________________________ ________________________\ / 2 | / 2 / 2 | / 2 | / 2 / 2 | | | | / x 2 / x / x 2 / x | / x 2 / x | / / 2\ / x 2 / x | / 2 / 2 | | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ / x | / x 2 / x | / 2\ | | | - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*\/ polar_lift\3 - y / - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | / x 2 / x | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | | / x 2 / x | | / x 2 / x | / 1 - ------------------ *|- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*polar_lift\3 - y / / 1 - ------------------ *|- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*polar_lift\3 - y / | | | / / 2\ / / 2\ / / 2\ / / 2\ | / / 2\ / / 2\ | / / 2\ / / 2\ |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | | / / 2\ / / 2\ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | / / 2\ | / / 2\ / / 2\ | / / 2\ | / / 2\ / / 2\ | | | | \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \/ polar_lift\3 - y / | / / 2\ / / 2\ | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | \ \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | | / | ________ | / 2 |-\/ 1 - x < | ________ | / 2 | -\/ 1 - x | / | | | | / _________________________ _________________________ _________________________ _________________________ | | | / 2 / 2 \ ____________________ / 2 \ ____________________ / 2 \ / 2 / 2 \ ____________________ / 2 \ / 2 / 2 \ / 2 / 2 \ | | | / x / 2\ | 12*x 4*x*y | 3 / / 2\ | 12*x 4*x*y | / / 2\ | 12*x 4*x*y | 2 / x / 2\ | 12*x 4*x*y | 2 / / 2\ | 12*x 4*x*y | / x / 2\ | 12*x 4*x*y | / x \ 2 / x / 2\ | 12*x 4*x*y | / x \ | | | 3*pi* / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------| 2*I*x *\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| 6*I*x*\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| pi*y * / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------| 2*I*x*y *\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| 6*I* / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------|*acosh|-----------------------| 2*I*y * / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------|*acosh|-----------------------| | | | / / 2\ | _________________________ _________________________ | | _________________________ _________________________ | | _________________________ _________________________ | / / 2\ | _________________________ _________________________ | | _________________________ _________________________ | / / 2\ | _________________________ _________________________ | | ____________________| / / 2\ | _________________________ _________________________ | | ____________________| | | | \/ polar_lift\3 - y / | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | / 2\ / x \ 2 / 2\ / x \ | | | | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / 6*I*x*\3 - y /*acosh|-----------------------| 2*I*x*y *\3 - y /*acosh|-----------------------| | | | ____________________ ____________________ ____________________ | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | ____________________| | ____________________| | | | / / 2\ 2 / / 2\ 2 / / 2\ / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ | | / / 2\ | | 2 | | | | 6*I*\/ polar_lift\3 - y / 6*I*x *\/ polar_lift\3 - y / 2*I*y *\/ polar_lift\3 - y / 6*I*\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / 2*I*y *\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / 3*pi*x*\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / pi*x*y *\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | x | | | |--------------------------------------------------------------------------- - --------------------------------------------------------------------------- - --------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------- for |-------| > 1 | | | _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ / _________________________ _________________________\ 2 2 / _________________________ _________________________\ 2 2 _________________________ / _________________________ _________________________\ 2 2 _________________________ / _________________________ _________________________\ 2 _________________________ / _________________________ _________________________\ _________________________ / _________________________ _________________________\ | 2| | | | / 2 / 2 / 2 / 2 / 2 / 2 | / 2 / 2 | ____________________ / _________________________ _________________________\ / _________________________ _________________________\ | / 2 / 2 | ____________________ / _________________________ _________________________\ / _________________________ _________________________\ / 2 | / 2 / 2 | / _________________________ _________________________\ / _________________________ _________________________\ / 2 | / 2 / 2 | / _________________________ _________________________\ / 2 | / 2 / 2 | / 2 | / 2 / 2 | |-3 + y | | | | / x 2 / x / x 2 / x / x 2 / x | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ | / 2 / 2 | / x | / x 2 / x | / 2\ / x | / x 2 / x | / 2\ | | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | / x 2 / x | | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | | | / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | / / 2\ | / / 2\ / / 2\ | | | | \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / |- | < dx otherwise | | | ________________________ ________________________ | | | ____________________ / 2 \ ____________________ / 2 \ ____________________ / 2 \ / 2 / 2 \ / 2 / 2 \ | | | 3 / / 2\ | 6*x 2*x*y | / / 2\ | 6*x 2*x*y | 2 / / 2\ | 6*x 2*x*y | / x / 2\ | 6*x 2*x*y | / x \ 2 / x / 2\ | 6*x 2*x*y | / x \ | | | x *\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| 3*x*\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| x*y *\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| 3* / 1 - ------------------ *\3 - y /*|- ------------------------------------------------- + -------------------------------------------------|*asin|-----------------------| y * / 1 - ------------------ *\3 - y /*|- ------------------------------------------------- + -------------------------------------------------|*asin|-----------------------| | | | | ________________________ ________________________ | | ________________________ ________________________ | | ________________________ ________________________ | / / 2\ | ________________________ ________________________ | | ____________________| / / 2\ | ________________________ ________________________ | | ____________________| | | | | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | / 2\ / x \ 2 / 2\ / x \ | | | | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / 3*x*\3 - y /*asin|-----------------------| x*y *\3 - y /*asin|-----------------------| | | | ____________________ ____________________ ____________________ | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | ____________________| | ____________________| | | | / / 2\ 2 / / 2\ / 2\ 2 / / 2\ | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ | | / / 2\ | | | | 3*\/ polar_lift\3 - y / y *\/ polar_lift\3 - y / 3*\3 - y / 3*x *\/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / y *\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | | | - ------------------------------------------------------------------------ + ------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- otherwise | | | ________________________ ________________________ ________________________ ________________________ / ________________________ ________________________\ ________________________ ________________________ 2 / ________________________ ________________________\ 2 2 2 2 ________________________ / ________________________ ________________________\ ________________________ / ________________________ ________________________\ | | | / 2 / 2 / 2 / 2 | / 2 / 2 | ____________________ / 2 / 2 / ________________________ ________________________\ | / 2 / 2 | ____________________ / ________________________ ________________________\ / ________________________ ________________________\ / ________________________ ________________________\ / ________________________ ________________________\ / 2 | / 2 / 2 | / 2 | / 2 / 2 | | | | / x 2 / x / x 2 / x | / x 2 / x | / / 2\ / x 2 / x | / 2 / 2 | | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ / x | / x 2 / x | / 2\ | | | - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*\/ polar_lift\3 - y / - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | / x 2 / x | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | | / x 2 / x | | / x 2 / x | / 1 - ------------------ *|- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*polar_lift\3 - y / / 1 - ------------------ *|- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*polar_lift\3 - y / | | | / / 2\ / / 2\ / / 2\ / / 2\ | / / 2\ / / 2\ | / / 2\ / / 2\ |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | | / / 2\ / / 2\ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | / / 2\ | / / 2\ / / 2\ | / / 2\ | / / 2\ / / 2\ | | | | \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \/ polar_lift\3 - y / | / / 2\ / / 2\ | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | \ \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | | / | ________ | / 2 \ \/ 1 - x
=
/ ________ | / 2 | \/ 1 - x | / | | | | / _________________________ _________________________ _________________________ _________________________ | | | / 2 / 2 \ ____________________ / 2 \ ____________________ / 2 \ / 2 / 2 \ ____________________ / 2 \ / 2 / 2 \ / 2 / 2 \ | | | / x / 2\ | 12*x 4*x*y | 3 / / 2\ | 12*x 4*x*y | / / 2\ | 12*x 4*x*y | 2 / x / 2\ | 12*x 4*x*y | 2 / / 2\ | 12*x 4*x*y | / x / 2\ | 12*x 4*x*y | / x \ 2 / x / 2\ | 12*x 4*x*y | / x \ | | | 3*pi* / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------| 2*I*x *\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| 6*I*x*\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| pi*y * / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------| 2*I*x*y *\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| 6*I* / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------|*acosh|-----------------------| 2*I*y * / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------|*acosh|-----------------------| | | | / / 2\ | _________________________ _________________________ | | _________________________ _________________________ | | _________________________ _________________________ | / / 2\ | _________________________ _________________________ | | _________________________ _________________________ | / / 2\ | _________________________ _________________________ | | ____________________| / / 2\ | _________________________ _________________________ | | ____________________| | | | \/ polar_lift\3 - y / | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | / 2\ / x \ 2 / 2\ / x \ | | | | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / 6*I*x*\3 - y /*acosh|-----------------------| 2*I*x*y *\3 - y /*acosh|-----------------------| | | | ____________________ ____________________ ____________________ | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | ____________________| | ____________________| | | | / / 2\ 2 / / 2\ 2 / / 2\ / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ | | / / 2\ | | 2 | | | | 6*I*\/ polar_lift\3 - y / 6*I*x *\/ polar_lift\3 - y / 2*I*y *\/ polar_lift\3 - y / 6*I*\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / 2*I*y *\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / 3*pi*x*\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / pi*x*y *\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | x | | | |--------------------------------------------------------------------------- - --------------------------------------------------------------------------- - --------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------- for |-------| > 1 | | | _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ / _________________________ _________________________\ 2 2 / _________________________ _________________________\ 2 2 _________________________ / _________________________ _________________________\ 2 2 _________________________ / _________________________ _________________________\ 2 _________________________ / _________________________ _________________________\ _________________________ / _________________________ _________________________\ | 2| | | | / 2 / 2 / 2 / 2 / 2 / 2 | / 2 / 2 | ____________________ / _________________________ _________________________\ / _________________________ _________________________\ | / 2 / 2 | ____________________ / _________________________ _________________________\ / _________________________ _________________________\ / 2 | / 2 / 2 | / _________________________ _________________________\ / _________________________ _________________________\ / 2 | / 2 / 2 | / _________________________ _________________________\ / 2 | / 2 / 2 | / 2 | / 2 / 2 | |-3 + y | | | | / x 2 / x / x 2 / x / x 2 / x | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ | / 2 / 2 | / x | / x 2 / x | / 2\ / x | / x 2 / x | / 2\ | | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | / x 2 / x | | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | | | / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | / / 2\ | / / 2\ / / 2\ | | | | \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / ________ ________ | | | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / / 2 / 2 | | < dx for \/ 1 - x > -\/ 1 - x | | | ________________________ ________________________ | | | ____________________ / 2 \ ____________________ / 2 \ ____________________ / 2 \ / 2 / 2 \ / 2 / 2 \ | | | 3 / / 2\ | 6*x 2*x*y | / / 2\ | 6*x 2*x*y | 2 / / 2\ | 6*x 2*x*y | / x / 2\ | 6*x 2*x*y | / x \ 2 / x / 2\ | 6*x 2*x*y | / x \ | | | x *\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| 3*x*\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| x*y *\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| 3* / 1 - ------------------ *\3 - y /*|- ------------------------------------------------- + -------------------------------------------------|*asin|-----------------------| y * / 1 - ------------------ *\3 - y /*|- ------------------------------------------------- + -------------------------------------------------|*asin|-----------------------| | | | | ________________________ ________________________ | | ________________________ ________________________ | | ________________________ ________________________ | / / 2\ | ________________________ ________________________ | | ____________________| / / 2\ | ________________________ ________________________ | | ____________________| | | | | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | / 2\ / x \ 2 / 2\ / x \ | | | | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / 3*x*\3 - y /*asin|-----------------------| x*y *\3 - y /*asin|-----------------------| | | | ____________________ ____________________ ____________________ | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | ____________________| | ____________________| | | | / / 2\ 2 / / 2\ / 2\ 2 / / 2\ | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ | | / / 2\ | | | | 3*\/ polar_lift\3 - y / y *\/ polar_lift\3 - y / 3*\3 - y / 3*x *\/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / y *\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | | | - ------------------------------------------------------------------------ + ------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- otherwise | | | ________________________ ________________________ ________________________ ________________________ / ________________________ ________________________\ ________________________ ________________________ 2 / ________________________ ________________________\ 2 2 2 2 ________________________ / ________________________ ________________________\ ________________________ / ________________________ ________________________\ | | | / 2 / 2 / 2 / 2 | / 2 / 2 | ____________________ / 2 / 2 / ________________________ ________________________\ | / 2 / 2 | ____________________ / ________________________ ________________________\ / ________________________ ________________________\ / ________________________ ________________________\ / ________________________ ________________________\ / 2 | / 2 / 2 | / 2 | / 2 / 2 | | | | / x 2 / x / x 2 / x | / x 2 / x | / / 2\ / x 2 / x | / 2 / 2 | | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ / x | / x 2 / x | / 2\ | | | - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*\/ polar_lift\3 - y / - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | / x 2 / x | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | | / x 2 / x | | / x 2 / x | / 1 - ------------------ *|- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*polar_lift\3 - y / / 1 - ------------------ *|- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*polar_lift\3 - y / | | | / / 2\ / / 2\ / / 2\ / / 2\ | / / 2\ / / 2\ | / / 2\ / / 2\ |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | | / / 2\ / / 2\ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | / / 2\ | / / 2\ / / 2\ | / / 2\ | / / 2\ / / 2\ | | | | \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \/ polar_lift\3 - y / | / / 2\ / / 2\ | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | \ \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | | / | ________ | / 2 |-\/ 1 - x < | ________ | / 2 | -\/ 1 - x | / | | | | / _________________________ _________________________ _________________________ _________________________ | | | / 2 / 2 \ ____________________ / 2 \ ____________________ / 2 \ / 2 / 2 \ ____________________ / 2 \ / 2 / 2 \ / 2 / 2 \ | | | / x / 2\ | 12*x 4*x*y | 3 / / 2\ | 12*x 4*x*y | / / 2\ | 12*x 4*x*y | 2 / x / 2\ | 12*x 4*x*y | 2 / / 2\ | 12*x 4*x*y | / x / 2\ | 12*x 4*x*y | / x \ 2 / x / 2\ | 12*x 4*x*y | / x \ | | | 3*pi* / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------| 2*I*x *\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| 6*I*x*\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| pi*y * / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------| 2*I*x*y *\/ polar_lift\3 - y / *|-------------------------------------------------- - --------------------------------------------------| 6*I* / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------|*acosh|-----------------------| 2*I*y * / -1 + ------------------ *\3 - y /*|-------------------------------------------------- - --------------------------------------------------|*acosh|-----------------------| | | | / / 2\ | _________________________ _________________________ | | _________________________ _________________________ | | _________________________ _________________________ | / / 2\ | _________________________ _________________________ | | _________________________ _________________________ | / / 2\ | _________________________ _________________________ | | ____________________| / / 2\ | _________________________ _________________________ | | ____________________| | | | \/ polar_lift\3 - y / | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | / 2\ / x \ 2 / 2\ / x \ | | | | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / 6*I*x*\3 - y /*acosh|-----------------------| 2*I*x*y *\3 - y /*acosh|-----------------------| | | | ____________________ ____________________ ____________________ | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | / -1 + ------------------ *polar_lift\3 - y / / -1 + ------------------ *polar_lift\3 - y /| | ____________________| | ____________________| | | | / / 2\ 2 / / 2\ 2 / / 2\ / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ | | / / 2\ | | 2 | | | | 6*I*\/ polar_lift\3 - y / 6*I*x *\/ polar_lift\3 - y / 2*I*y *\/ polar_lift\3 - y / 6*I*\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / 2*I*y *\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / 3*pi*x*\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / pi*x*y *\3 - y / \\/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | x | | | |--------------------------------------------------------------------------- - --------------------------------------------------------------------------- - --------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------- for |-------| > 1 | | | _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ / _________________________ _________________________\ 2 2 / _________________________ _________________________\ 2 2 _________________________ / _________________________ _________________________\ 2 2 _________________________ / _________________________ _________________________\ 2 _________________________ / _________________________ _________________________\ _________________________ / _________________________ _________________________\ | 2| | | | / 2 / 2 / 2 / 2 / 2 / 2 | / 2 / 2 | ____________________ / _________________________ _________________________\ / _________________________ _________________________\ | / 2 / 2 | ____________________ / _________________________ _________________________\ / _________________________ _________________________\ / 2 | / 2 / 2 | / _________________________ _________________________\ / _________________________ _________________________\ / 2 | / 2 / 2 | / _________________________ _________________________\ / 2 | / 2 / 2 | / 2 | / 2 / 2 | |-3 + y | | | | / x 2 / x / x 2 / x / x 2 / x | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ | / 2 / 2 | / x | / x 2 / x | / 2\ / x | / x 2 / x | / 2\ | | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ - 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | / x 2 / x | | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | / x 2 / x | / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / / -1 + ------------------ *|- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ |*polar_lift\3 - y / | | | / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | |- 12* / -1 + ------------------ + 4*y * / -1 + ------------------ | / / 2\ | / / 2\ / / 2\ | / / 2\ | / / 2\ / / 2\ | | | | \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / |- | < dx otherwise | | | ________________________ ________________________ | | | ____________________ / 2 \ ____________________ / 2 \ ____________________ / 2 \ / 2 / 2 \ / 2 / 2 \ | | | 3 / / 2\ | 6*x 2*x*y | / / 2\ | 6*x 2*x*y | 2 / / 2\ | 6*x 2*x*y | / x / 2\ | 6*x 2*x*y | / x \ 2 / x / 2\ | 6*x 2*x*y | / x \ | | | x *\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| 3*x*\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| x*y *\/ polar_lift\3 - y / *|- ------------------------------------------------- + -------------------------------------------------| 3* / 1 - ------------------ *\3 - y /*|- ------------------------------------------------- + -------------------------------------------------|*asin|-----------------------| y * / 1 - ------------------ *\3 - y /*|- ------------------------------------------------- + -------------------------------------------------|*asin|-----------------------| | | | | ________________________ ________________________ | | ________________________ ________________________ | | ________________________ ________________________ | / / 2\ | ________________________ ________________________ | | ____________________| / / 2\ | ________________________ ________________________ | | ____________________| | | | | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | \/ polar_lift\3 - y / | / 2 / 2 | | / / 2\ | / 2\ / x \ 2 / 2\ / x \ | | | | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / | / x / 2\ / x / 2\| \\/ polar_lift\3 - y / / 3*x*\3 - y /*asin|-----------------------| x*y *\3 - y /*asin|-----------------------| | | | ____________________ ____________________ ____________________ | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | / 1 - ------------------ *polar_lift\3 - y / / 1 - ------------------ *polar_lift\3 - y /| | ____________________| | ____________________| | | | / / 2\ 2 / / 2\ / 2\ 2 / / 2\ | / / 2\ / / 2\ | 2 / 2\ | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ | | / / 2\ | | | | 3*\/ polar_lift\3 - y / y *\/ polar_lift\3 - y / 3*\3 - y / 3*x *\/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / y *\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / \\/ polar_lift\3 - y / / | | | - ------------------------------------------------------------------------ + ------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- otherwise | | | ________________________ ________________________ ________________________ ________________________ / ________________________ ________________________\ ________________________ ________________________ 2 / ________________________ ________________________\ 2 2 2 2 ________________________ / ________________________ ________________________\ ________________________ / ________________________ ________________________\ | | | / 2 / 2 / 2 / 2 | / 2 / 2 | ____________________ / 2 / 2 / ________________________ ________________________\ | / 2 / 2 | ____________________ / ________________________ ________________________\ / ________________________ ________________________\ / ________________________ ________________________\ / ________________________ ________________________\ / 2 | / 2 / 2 | / 2 | / 2 / 2 | | | | / x 2 / x / x 2 / x | / x 2 / x | / / 2\ / x 2 / x | / 2 / 2 | | / x 2 / x | / / 2\ | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | | / 2 / 2 | / x | / x 2 / x | / 2\ / x | / x 2 / x | / 2\ | | | - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*\/ polar_lift\3 - y / - 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | / x 2 / x | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*\/ polar_lift\3 - y / | / x 2 / x | | / x 2 / x | | / x 2 / x | | / x 2 / x | / 1 - ------------------ *|- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*polar_lift\3 - y / / 1 - ------------------ *|- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ |*polar_lift\3 - y / | | | / / 2\ / / 2\ / / 2\ / / 2\ | / / 2\ / / 2\ | / / 2\ / / 2\ |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | | / / 2\ / / 2\ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | |- 6* / 1 - ------------------ + 2*y * / 1 - ------------------ | / / 2\ | / / 2\ / / 2\ | / / 2\ | / / 2\ / / 2\ | | | | \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \/ polar_lift\3 - y / | / / 2\ / / 2\ | \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | | / / 2\ / / 2\ | \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \/ polar_lift\3 - y / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | \ \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / \ \/ polar_lift\3 - y / \/ polar_lift\3 - y / / | | | / | ________ | / 2 \ \/ 1 - x
Piecewise((Integral(Piecewise((6*i*sqrt(polar_lift(3 - y^2))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))) - 6*i*x^2*sqrt(polar_lift(3 - y^2))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))) - 2*i*y^2*sqrt(polar_lift(3 - y^2))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))) + 6*i*(3 - y^2)/((-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*sqrt(polar_lift(3 - y^2))) - 3*pi*sqrt(-1 + x^2/polar_lift(3 - y^2))*(3 - y^2)*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 - 2*i*x^3*sqrt(polar_lift(3 - y^2))*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 - 2*i*y^2*(3 - y^2)/((-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*sqrt(polar_lift(3 - y^2))) + 6*i*x*sqrt(polar_lift(3 - y^2))*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 + pi*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))*(3 - y^2)*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 - 3*pi*x*(3 - y^2)/(sqrt(-1 + x^2/polar_lift(3 - y^2))*(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)) - 2*i*x*y^2*sqrt(polar_lift(3 - y^2))*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 + 6*i*sqrt(-1 + x^2/polar_lift(3 - y^2))*(3 - y^2)*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))*acosh(x/sqrt(polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 + pi*x*y^2*(3 - y^2)/(sqrt(-1 + x^2/polar_lift(3 - y^2))*(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)) - 2*i*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))*(3 - y^2)*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))*acosh(x/sqrt(polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 + 6*i*x*(3 - y^2)*acosh(x/sqrt(polar_lift(3 - y^2)))/(sqrt(-1 + x^2/polar_lift(3 - y^2))*(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)) - 2*i*x*y^2*(3 - y^2)*acosh(x/sqrt(polar_lift(3 - y^2)))/(sqrt(-1 + x^2/polar_lift(3 - y^2))*(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)), Abs(x^2/(-3 + y^2)) > 1), (-3*sqrt(polar_lift(3 - y^2))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2))) + y^2*sqrt(polar_lift(3 - y^2))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2))) - 3*(3 - y^2)/((-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))*sqrt(polar_lift(3 - y^2))) + 3*x^2*sqrt(polar_lift(3 - y^2))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2))) + x^3*sqrt(polar_lift(3 - y^2))*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 + y^2*(3 - y^2)/((-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))*sqrt(polar_lift(3 - y^2))) - 3*x*sqrt(polar_lift(3 - y^2))*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 + x*y^2*sqrt(polar_lift(3 - y^2))*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 - 3*sqrt(1 - x^2/polar_lift(3 - y^2))*(3 - y^2)*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))*asin(x/sqrt(polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 + y^2*sqrt(1 - x^2/polar_lift(3 - y^2))*(3 - y^2)*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))*asin(x/sqrt(polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 + 3*x*(3 - y^2)*asin(x/sqrt(polar_lift(3 - y^2)))/(sqrt(1 - x^2/polar_lift(3 - y^2))*(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)) - x*y^2*(3 - y^2)*asin(x/sqrt(polar_lift(3 - y^2)))/(sqrt(1 - x^2/polar_lift(3 - y^2))*(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)), True)), (x, -sqrt(1 - x^2), sqrt(1 - x^2))), sqrt(1 - x^2) > -sqrt(1 - x^2)), (-Integral(Piecewise((6*i*sqrt(polar_lift(3 - y^2))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))) - 6*i*x^2*sqrt(polar_lift(3 - y^2))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))) - 2*i*y^2*sqrt(polar_lift(3 - y^2))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))) + 6*i*(3 - y^2)/((-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*sqrt(polar_lift(3 - y^2))) - 3*pi*sqrt(-1 + x^2/polar_lift(3 - y^2))*(3 - y^2)*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 - 2*i*x^3*sqrt(polar_lift(3 - y^2))*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 - 2*i*y^2*(3 - y^2)/((-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*sqrt(polar_lift(3 - y^2))) + 6*i*x*sqrt(polar_lift(3 - y^2))*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 + pi*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))*(3 - y^2)*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 - 3*pi*x*(3 - y^2)/(sqrt(-1 + x^2/polar_lift(3 - y^2))*(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)) - 2*i*x*y^2*sqrt(polar_lift(3 - y^2))*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 + 6*i*sqrt(-1 + x^2/polar_lift(3 - y^2))*(3 - y^2)*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))*acosh(x/sqrt(polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 + pi*x*y^2*(3 - y^2)/(sqrt(-1 + x^2/polar_lift(3 - y^2))*(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)) - 2*i*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2))*(3 - y^2)*(12*x/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) - 4*x*y^2/(sqrt(-1 + x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))*acosh(x/sqrt(polar_lift(3 - y^2)))/(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))^2 + 6*i*x*(3 - y^2)*acosh(x/sqrt(polar_lift(3 - y^2)))/(sqrt(-1 + x^2/polar_lift(3 - y^2))*(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)) - 2*i*x*y^2*(3 - y^2)*acosh(x/sqrt(polar_lift(3 - y^2)))/(sqrt(-1 + x^2/polar_lift(3 - y^2))*(-12*sqrt(-1 + x^2/polar_lift(3 - y^2)) + 4*y^2*sqrt(-1 + x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)), Abs(x^2/(-3 + y^2)) > 1), (-3*sqrt(polar_lift(3 - y^2))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2))) + y^2*sqrt(polar_lift(3 - y^2))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2))) - 3*(3 - y^2)/((-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))*sqrt(polar_lift(3 - y^2))) + 3*x^2*sqrt(polar_lift(3 - y^2))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2))) + x^3*sqrt(polar_lift(3 - y^2))*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 + y^2*(3 - y^2)/((-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))*sqrt(polar_lift(3 - y^2))) - 3*x*sqrt(polar_lift(3 - y^2))*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 + x*y^2*sqrt(polar_lift(3 - y^2))*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 - 3*sqrt(1 - x^2/polar_lift(3 - y^2))*(3 - y^2)*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))*asin(x/sqrt(polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 + y^2*sqrt(1 - x^2/polar_lift(3 - y^2))*(3 - y^2)*(-6*x/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)) + 2*x*y^2/(sqrt(1 - x^2/polar_lift(3 - y^2))*polar_lift(3 - y^2)))*asin(x/sqrt(polar_lift(3 - y^2)))/(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))^2 + 3*x*(3 - y^2)*asin(x/sqrt(polar_lift(3 - y^2)))/(sqrt(1 - x^2/polar_lift(3 - y^2))*(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)) - x*y^2*(3 - y^2)*asin(x/sqrt(polar_lift(3 - y^2)))/(sqrt(1 - x^2/polar_lift(3 - y^2))*(-6*sqrt(1 - x^2/polar_lift(3 - y^2)) + 2*y^2*sqrt(1 - x^2/polar_lift(3 - y^2)))*polar_lift(3 - y^2)), True)), (x, sqrt(1 - x^2), -sqrt(1 - x^2))), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.