Integral de xy(1-x-y)^1/2 dx
Solución
Respuesta (Indefinida)
[src]
/
| / 5/2 3/2 3/2\
| ___________ | (1 - x - y) (1 - x - y) y*(1 - x - y) |
| x*y*\/ 1 - x - y dx = C - 2*y*|- -------------- + -------------- - ----------------|
| \ 5 3 3 /
/
∫xy−y+(1−x)dx=C−2y(−3y(−x−y+1)23−5(−x−y+1)25+3(−x−y+1)23)
/ 0
| /
| |
| | / / ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ \
| | | | / x 5/2 / x 3/2 / x 5/2 / x 5/2 3 / x ___________________ 2 / x ___________________ / x 3/2 / x ___________________ / x 3/2 2 / x ___________________ / x 5/2 / x 3/2 2 / x 3/2 / x 3/2 / x ___________________ 2 / x ___________________|
| | | | 5/2 5/2 5/2 5/2 60*I* / -1 + ----------------- *polar_lift (1 - y) 8*I* / -1 + ----------------- *polar_lift (1 - y) 3/2 6*I* / -1 + ----------------- *polar_lift (1 - y) 90*I*x* / -1 + ----------------- *polar_lift (1 - y) 90*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 60*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 24*I*x* / -1 + ----------------- *polar_lift (1 - y) 2 ___________________ ___________________ 3/2 2 3/2 3 8*I*x* / -1 + ----------------- *\/ polar_lift(1 - y) 8*I*y* / -1 + ----------------- *polar_lift (1 - y) 18*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 60*I*y* / -1 + ----------------- *polar_lift (1 - y) 120*I*x* / -1 + ----------------- *polar_lift (1 - y) 180*I*x * / -1 + ----------------- *polar_lift (1 - y) 120*I*x*y* / -1 + ----------------- *polar_lift (1 - y) 8*I*x*y* / -1 + ----------------- *\/ polar_lift(1 - y) 2 ___________________ 60*I*y*x * / -1 + ----------------- *\/ polar_lift(1 - y) |
| | | |4*polar_lift (1 - y) 60*polar_lift (1 - y) 60*x*polar_lift (1 - y) 60*y*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*I*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 6*I*x *\/ polar_lift(1 - y) 4*I*x*\/ polar_lift(1 - y) 2*I*y*polar_lift (1 - y) 2*I*x 3*I*x*polar_lift (1 - y) 3*I*x \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*I*y*x 4*I*x*y*\/ polar_lift(1 - y) \/ polar_lift(1 - y) | | x |
| | |y*|---------------------- + ----------------------- - ------------------------- - ------------------------- - ------------------------------------------------------ - ----------------------------------------------------- + ------------------------------------------------ + ----------------------------------------------------- - -------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------ - ------------------------------------------------ - ------------------------------------------------ + ---------------------------------------------------------------------- + ------------------------------------------------ + ---------------------------------------------------------------------- + -------------------------------------------------------- + ------------------------------------------------------- + ---------------------------------------------------------- + -------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------- - ----------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------ + ------------------------------------------------------------| for |------| > 1
| | | | -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y ________________________ -15 + 15*x + 15*y 2 2 2 -15 + 15*x + 15*y ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ -15 + 15*x + 15*y -15 + 15*x + 15*y -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y ________________________ ________________________ 2 | |-1 + y|
| | | | (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x / x / x ___________________ / x / x ___________________ (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x ___________________ / x (-15 + 15*x + 15*y) |
| | | | / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y) |
| | | \ \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) /
|- | < dx for -1 + y > 0
| | | / _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ \
| | | | / x 5/2 / x 3/2 / x 5/2 / x 5/2 3 / x ___________________ 2 / x ___________________ / x 3/2 / x ___________________ / x 3/2 2 / x ___________________ / x 5/2 / x 3/2 2 / x 3/2 / x 3/2 / x ___________________ 2 / x ___________________|
| | | | 5/2 5/2 5/2 5/2 60* / 1 - ----------------- *polar_lift (1 - y) 8* / 1 - ----------------- *polar_lift (1 - y) 3/2 6* / 1 - ----------------- *polar_lift (1 - y) 90*x* / 1 - ----------------- *polar_lift (1 - y) 90*x * / 1 - ----------------- *\/ polar_lift(1 - y) 60*x * / 1 - ----------------- *\/ polar_lift(1 - y) 24*x* / 1 - ----------------- *polar_lift (1 - y) 3/2 3 2 3/2 ___________________ 2 ___________________ 8*x* / 1 - ----------------- *\/ polar_lift(1 - y) 8*y* / 1 - ----------------- *polar_lift (1 - y) 18*x * / 1 - ----------------- *\/ polar_lift(1 - y) 60*y* / 1 - ----------------- *polar_lift (1 - y) 120*x* / 1 - ----------------- *polar_lift (1 - y) 180*x * / 1 - ----------------- *polar_lift (1 - y) 120*x*y* / 1 - ----------------- *polar_lift (1 - y) 8*x*y* / 1 - ----------------- *\/ polar_lift(1 - y) ___________________ 2 60*y*x * / 1 - ----------------- *\/ polar_lift(1 - y) |
| | | |4*polar_lift (1 - y) 60*polar_lift (1 - y) 60*x*polar_lift (1 - y) 60*y*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 3*x*polar_lift (1 - y) 3*x 2*x 2*y*polar_lift (1 - y) 4*x*\/ polar_lift(1 - y) 6*x *\/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 4*x*y*\/ polar_lift(1 - y) 2*y*x \/ polar_lift(1 - y) |
| | | y*|---------------------- + ----------------------- - ------------------------- - ------------------------- - --------------------------------------------------- - -------------------------------------------------- - ----------------------------------------------- + -------------------------------------------------- - ----------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------- - --------------------------------------------------------------------- - --------------------------------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------------- + ---------------------------------------------------- + ------------------------------------------------------- + ----------------------------------------------------- + ------------------------------------------------------ + ------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------- + --------------------------------------------------------------------- + ---------------------------------------------------------| otherwise
| | | | -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y _______________________ -15 + 15*x + 15*y 2 2 2 -15 + 15*x + 15*y _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ -15 + 15*x + 15*y -15 + 15*x + 15*y -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y _______________________ _______________________ 2 |
| | | | (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x ___________________ / x ___________________ / x / x / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x ___________________ (-15 + 15*x + 15*y) |
| | | | / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) |
| | \ \ \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) /
| |
| /
| 1 - y
<
| 1 - y
| /
| |
| | / / ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ \
| | | | / x 5/2 / x 3/2 / x 5/2 / x 5/2 3 / x ___________________ 2 / x ___________________ / x 3/2 / x ___________________ / x 3/2 2 / x ___________________ / x 5/2 / x 3/2 2 / x 3/2 / x 3/2 / x ___________________ 2 / x ___________________|
| | | | 5/2 5/2 5/2 5/2 60*I* / -1 + ----------------- *polar_lift (1 - y) 8*I* / -1 + ----------------- *polar_lift (1 - y) 3/2 6*I* / -1 + ----------------- *polar_lift (1 - y) 90*I*x* / -1 + ----------------- *polar_lift (1 - y) 90*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 60*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 24*I*x* / -1 + ----------------- *polar_lift (1 - y) 2 ___________________ ___________________ 3/2 2 3/2 3 8*I*x* / -1 + ----------------- *\/ polar_lift(1 - y) 8*I*y* / -1 + ----------------- *polar_lift (1 - y) 18*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 60*I*y* / -1 + ----------------- *polar_lift (1 - y) 120*I*x* / -1 + ----------------- *polar_lift (1 - y) 180*I*x * / -1 + ----------------- *polar_lift (1 - y) 120*I*x*y* / -1 + ----------------- *polar_lift (1 - y) 8*I*x*y* / -1 + ----------------- *\/ polar_lift(1 - y) 2 ___________________ 60*I*y*x * / -1 + ----------------- *\/ polar_lift(1 - y) |
| | | |4*polar_lift (1 - y) 60*polar_lift (1 - y) 60*x*polar_lift (1 - y) 60*y*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*I*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 6*I*x *\/ polar_lift(1 - y) 4*I*x*\/ polar_lift(1 - y) 2*I*y*polar_lift (1 - y) 2*I*x 3*I*x*polar_lift (1 - y) 3*I*x \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*I*y*x 4*I*x*y*\/ polar_lift(1 - y) \/ polar_lift(1 - y) | | x |
| | |y*|---------------------- + ----------------------- - ------------------------- - ------------------------- - ------------------------------------------------------ - ----------------------------------------------------- + ------------------------------------------------ + ----------------------------------------------------- - -------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------ - ------------------------------------------------ - ------------------------------------------------ + ---------------------------------------------------------------------- + ------------------------------------------------ + ---------------------------------------------------------------------- + -------------------------------------------------------- + ------------------------------------------------------- + ---------------------------------------------------------- + -------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------- - ----------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------ + ------------------------------------------------------------| for |------| > 1
| | | | -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y ________________________ -15 + 15*x + 15*y 2 2 2 -15 + 15*x + 15*y ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ -15 + 15*x + 15*y -15 + 15*x + 15*y -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y ________________________ ________________________ 2 | |-1 + y|
| | | | (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x / x / x ___________________ / x / x ___________________ (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x ___________________ / x (-15 + 15*x + 15*y) |
| | | | / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y) |
| | | \ \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) /
| | < dx otherwise
| | | / _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ \
| | | | / x 5/2 / x 3/2 / x 5/2 / x 5/2 3 / x ___________________ 2 / x ___________________ / x 3/2 / x ___________________ / x 3/2 2 / x ___________________ / x 5/2 / x 3/2 2 / x 3/2 / x 3/2 / x ___________________ 2 / x ___________________|
| | | | 5/2 5/2 5/2 5/2 60* / 1 - ----------------- *polar_lift (1 - y) 8* / 1 - ----------------- *polar_lift (1 - y) 3/2 6* / 1 - ----------------- *polar_lift (1 - y) 90*x* / 1 - ----------------- *polar_lift (1 - y) 90*x * / 1 - ----------------- *\/ polar_lift(1 - y) 60*x * / 1 - ----------------- *\/ polar_lift(1 - y) 24*x* / 1 - ----------------- *polar_lift (1 - y) 3/2 3 2 3/2 ___________________ 2 ___________________ 8*x* / 1 - ----------------- *\/ polar_lift(1 - y) 8*y* / 1 - ----------------- *polar_lift (1 - y) 18*x * / 1 - ----------------- *\/ polar_lift(1 - y) 60*y* / 1 - ----------------- *polar_lift (1 - y) 120*x* / 1 - ----------------- *polar_lift (1 - y) 180*x * / 1 - ----------------- *polar_lift (1 - y) 120*x*y* / 1 - ----------------- *polar_lift (1 - y) 8*x*y* / 1 - ----------------- *\/ polar_lift(1 - y) ___________________ 2 60*y*x * / 1 - ----------------- *\/ polar_lift(1 - y) |
| | | |4*polar_lift (1 - y) 60*polar_lift (1 - y) 60*x*polar_lift (1 - y) 60*y*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 3*x*polar_lift (1 - y) 3*x 2*x 2*y*polar_lift (1 - y) 4*x*\/ polar_lift(1 - y) 6*x *\/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 4*x*y*\/ polar_lift(1 - y) 2*y*x \/ polar_lift(1 - y) |
| | | y*|---------------------- + ----------------------- - ------------------------- - ------------------------- - --------------------------------------------------- - -------------------------------------------------- - ----------------------------------------------- + -------------------------------------------------- - ----------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------- - --------------------------------------------------------------------- - --------------------------------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------------- + ---------------------------------------------------- + ------------------------------------------------------- + ----------------------------------------------------- + ------------------------------------------------------ + ------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------- + --------------------------------------------------------------------- + ---------------------------------------------------------| otherwise
| | | | -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y _______________________ -15 + 15*x + 15*y 2 2 2 -15 + 15*x + 15*y _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ -15 + 15*x + 15*y -15 + 15*x + 15*y -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y _______________________ _______________________ 2 |
| | | | (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x ___________________ / x ___________________ / x / x / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x ___________________ (-15 + 15*x + 15*y) |
| | | | / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) |
| | \ \ \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) /
| |
| /
\ 0
⎩⎨⎧−1−y∫0⎩⎨⎧y(−(15x+15y−15)290ix3polar_lift(1−y)x−1polar_lift(1−y)+polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)3ix3+(15x+15y−15)260ix2ypolar_lift(1−y)x−1polar_lift(1−y)−polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)2ix2y+15x+15y−1518ix2polar_lift(1−y)x−1polar_lift(1−y)+(15x+15y−15)2180ix2polar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260ix2polar_lift(1−y)x−1polar_lift(1−y)−polar_lift(1−y)x−1(15x+15y−15)6ix2polar_lift(1−y)+polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)2ix2−15x+15y−158ixypolar_lift(1−y)x−1polar_lift(1−y)−(15x+15y−15)2120ixypolar_lift(1−y)x−1polar_lift23(1−y)+polar_lift(1−y)x−1(15x+15y−15)4ixypolar_lift(1−y)−15x+15y−1524ixpolar_lift(1−y)x−1polar_lift23(1−y)+15x+15y−158ixpolar_lift(1−y)x−1polar_lift(1−y)−(15x+15y−15)290ixpolar_lift(1−y)x−1polar_lift25(1−y)+(15x+15y−15)2120ixpolar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260xpolar_lift25(1−y)+polar_lift(1−y)x−1(15x+15y−15)3ixpolar_lift23(1−y)−polar_lift(1−y)x−1(15x+15y−15)4ixpolar_lift(1−y)+15x+15y−158iypolar_lift(1−y)x−1polar_lift23(1−y)+(15x+15y−15)260iypolar_lift(1−y)x−1polar_lift25(1−y)−(15x+15y−15)260ypolar_lift25(1−y)−polar_lift(1−y)x−1(15x+15y−15)2iypolar_lift23(1−y)+15x+15y−156ipolar_lift(1−y)x−1polar_lift25(1−y)−15x+15y−158ipolar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260ipolar_lift(1−y)x−1polar_lift25(1−y)+15x+15y−154polar_lift25(1−y)+(15x+15y−15)260polar_lift25(1−y)+polar_lift(1−y)x−1(15x+15y−15)2ipolar_lift23(1−y))y(−(15x+15y−15)290x3−polar_lift(1−y)x+1polar_lift(1−y)−−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)3x3+(15x+15y−15)260x2y−polar_lift(1−y)x+1polar_lift(1−y)+−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)2x2y+15x+15y−1518x2−polar_lift(1−y)x+1polar_lift(1−y)+(15x+15y−15)2180x2−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260x2−polar_lift(1−y)x+1polar_lift(1−y)+−polar_lift(1−y)x+1(15x+15y−15)6x2polar_lift(1−y)−−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)2x2−15x+15y−158xy−polar_lift(1−y)x+1polar_lift(1−y)−(15x+15y−15)2120xy−polar_lift(1−y)x+1polar_lift23(1−y)−−polar_lift(1−y)x+1(15x+15y−15)4xypolar_lift(1−y)−15x+15y−1524x−polar_lift(1−y)x+1polar_lift23(1−y)+15x+15y−158x−polar_lift(1−y)x+1polar_lift(1−y)−(15x+15y−15)290x−polar_lift(1−y)x+1polar_lift25(1−y)+(15x+15y−15)2120x−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260xpolar_lift25(1−y)−−polar_lift(1−y)x+1(15x+15y−15)3xpolar_lift23(1−y)+−polar_lift(1−y)x+1(15x+15y−15)4xpolar_lift(1−y)+15x+15y−158y−polar_lift(1−y)x+1polar_lift23(1−y)+(15x+15y−15)260y−polar_lift(1−y)x+1polar_lift25(1−y)−(15x+15y−15)260ypolar_lift25(1−y)+−polar_lift(1−y)x+1(15x+15y−15)2ypolar_lift23(1−y)+15x+15y−156−polar_lift(1−y)x+1polar_lift25(1−y)−15x+15y−158−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260−polar_lift(1−y)x+1polar_lift25(1−y)+15x+15y−154polar_lift25(1−y)+(15x+15y−15)260polar_lift25(1−y)−−polar_lift(1−y)x+1(15x+15y−15)2polar_lift23(1−y))fory−1x>1otherwisedx0∫1−y⎩⎨⎧y(−(15x+15y−15)290ix3polar_lift(1−y)x−1polar_lift(1−y)+polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)3ix3+(15x+15y−15)260ix2ypolar_lift(1−y)x−1polar_lift(1−y)−polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)2ix2y+15x+15y−1518ix2polar_lift(1−y)x−1polar_lift(1−y)+(15x+15y−15)2180ix2polar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260ix2polar_lift(1−y)x−1polar_lift(1−y)−polar_lift(1−y)x−1(15x+15y−15)6ix2polar_lift(1−y)+polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)2ix2−15x+15y−158ixypolar_lift(1−y)x−1polar_lift(1−y)−(15x+15y−15)2120ixypolar_lift(1−y)x−1polar_lift23(1−y)+polar_lift(1−y)x−1(15x+15y−15)4ixypolar_lift(1−y)−15x+15y−1524ixpolar_lift(1−y)x−1polar_lift23(1−y)+15x+15y−158ixpolar_lift(1−y)x−1polar_lift(1−y)−(15x+15y−15)290ixpolar_lift(1−y)x−1polar_lift25(1−y)+(15x+15y−15)2120ixpolar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260xpolar_lift25(1−y)+polar_lift(1−y)x−1(15x+15y−15)3ixpolar_lift23(1−y)−polar_lift(1−y)x−1(15x+15y−15)4ixpolar_lift(1−y)+15x+15y−158iypolar_lift(1−y)x−1polar_lift23(1−y)+(15x+15y−15)260iypolar_lift(1−y)x−1polar_lift25(1−y)−(15x+15y−15)260ypolar_lift25(1−y)−polar_lift(1−y)x−1(15x+15y−15)2iypolar_lift23(1−y)+15x+15y−156ipolar_lift(1−y)x−1polar_lift25(1−y)−15x+15y−158ipolar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260ipolar_lift(1−y)x−1polar_lift25(1−y)+15x+15y−154polar_lift25(1−y)+(15x+15y−15)260polar_lift25(1−y)+polar_lift(1−y)x−1(15x+15y−15)2ipolar_lift23(1−y))y(−(15x+15y−15)290x3−polar_lift(1−y)x+1polar_lift(1−y)−−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)3x3+(15x+15y−15)260x2y−polar_lift(1−y)x+1polar_lift(1−y)+−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)2x2y+15x+15y−1518x2−polar_lift(1−y)x+1polar_lift(1−y)+(15x+15y−15)2180x2−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260x2−polar_lift(1−y)x+1polar_lift(1−y)+−polar_lift(1−y)x+1(15x+15y−15)6x2polar_lift(1−y)−−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)2x2−15x+15y−158xy−polar_lift(1−y)x+1polar_lift(1−y)−(15x+15y−15)2120xy−polar_lift(1−y)x+1polar_lift23(1−y)−−polar_lift(1−y)x+1(15x+15y−15)4xypolar_lift(1−y)−15x+15y−1524x−polar_lift(1−y)x+1polar_lift23(1−y)+15x+15y−158x−polar_lift(1−y)x+1polar_lift(1−y)−(15x+15y−15)290x−polar_lift(1−y)x+1polar_lift25(1−y)+(15x+15y−15)2120x−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260xpolar_lift25(1−y)−−polar_lift(1−y)x+1(15x+15y−15)3xpolar_lift23(1−y)+−polar_lift(1−y)x+1(15x+15y−15)4xpolar_lift(1−y)+15x+15y−158y−polar_lift(1−y)x+1polar_lift23(1−y)+(15x+15y−15)260y−polar_lift(1−y)x+1polar_lift25(1−y)−(15x+15y−15)260ypolar_lift25(1−y)+−polar_lift(1−y)x+1(15x+15y−15)2ypolar_lift23(1−y)+15x+15y−156−polar_lift(1−y)x+1polar_lift25(1−y)−15x+15y−158−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260−polar_lift(1−y)x+1polar_lift25(1−y)+15x+15y−154polar_lift25(1−y)+(15x+15y−15)260polar_lift25(1−y)−−polar_lift(1−y)x+1(15x+15y−15)2polar_lift23(1−y))fory−1x>1otherwisedxfory−1>0otherwise
=
/ 0
| /
| |
| | / / ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ \
| | | | / x 5/2 / x 3/2 / x 5/2 / x 5/2 3 / x ___________________ 2 / x ___________________ / x 3/2 / x ___________________ / x 3/2 2 / x ___________________ / x 5/2 / x 3/2 2 / x 3/2 / x 3/2 / x ___________________ 2 / x ___________________|
| | | | 5/2 5/2 5/2 5/2 60*I* / -1 + ----------------- *polar_lift (1 - y) 8*I* / -1 + ----------------- *polar_lift (1 - y) 3/2 6*I* / -1 + ----------------- *polar_lift (1 - y) 90*I*x* / -1 + ----------------- *polar_lift (1 - y) 90*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 60*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 24*I*x* / -1 + ----------------- *polar_lift (1 - y) 2 ___________________ ___________________ 3/2 2 3/2 3 8*I*x* / -1 + ----------------- *\/ polar_lift(1 - y) 8*I*y* / -1 + ----------------- *polar_lift (1 - y) 18*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 60*I*y* / -1 + ----------------- *polar_lift (1 - y) 120*I*x* / -1 + ----------------- *polar_lift (1 - y) 180*I*x * / -1 + ----------------- *polar_lift (1 - y) 120*I*x*y* / -1 + ----------------- *polar_lift (1 - y) 8*I*x*y* / -1 + ----------------- *\/ polar_lift(1 - y) 2 ___________________ 60*I*y*x * / -1 + ----------------- *\/ polar_lift(1 - y) |
| | | |4*polar_lift (1 - y) 60*polar_lift (1 - y) 60*x*polar_lift (1 - y) 60*y*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*I*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 6*I*x *\/ polar_lift(1 - y) 4*I*x*\/ polar_lift(1 - y) 2*I*y*polar_lift (1 - y) 2*I*x 3*I*x*polar_lift (1 - y) 3*I*x \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*I*y*x 4*I*x*y*\/ polar_lift(1 - y) \/ polar_lift(1 - y) | | x |
| | |y*|---------------------- + ----------------------- - ------------------------- - ------------------------- - ------------------------------------------------------ - ----------------------------------------------------- + ------------------------------------------------ + ----------------------------------------------------- - -------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------ - ------------------------------------------------ - ------------------------------------------------ + ---------------------------------------------------------------------- + ------------------------------------------------ + ---------------------------------------------------------------------- + -------------------------------------------------------- + ------------------------------------------------------- + ---------------------------------------------------------- + -------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------- - ----------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------ + ------------------------------------------------------------| for |------| > 1
| | | | -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y ________________________ -15 + 15*x + 15*y 2 2 2 -15 + 15*x + 15*y ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ -15 + 15*x + 15*y -15 + 15*x + 15*y -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y ________________________ ________________________ 2 | |-1 + y|
| | | | (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x / x / x ___________________ / x / x ___________________ (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x ___________________ / x (-15 + 15*x + 15*y) |
| | | | / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y) |
| | | \ \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) /
|- | < dx for -1 + y > 0
| | | / _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ \
| | | | / x 5/2 / x 3/2 / x 5/2 / x 5/2 3 / x ___________________ 2 / x ___________________ / x 3/2 / x ___________________ / x 3/2 2 / x ___________________ / x 5/2 / x 3/2 2 / x 3/2 / x 3/2 / x ___________________ 2 / x ___________________|
| | | | 5/2 5/2 5/2 5/2 60* / 1 - ----------------- *polar_lift (1 - y) 8* / 1 - ----------------- *polar_lift (1 - y) 3/2 6* / 1 - ----------------- *polar_lift (1 - y) 90*x* / 1 - ----------------- *polar_lift (1 - y) 90*x * / 1 - ----------------- *\/ polar_lift(1 - y) 60*x * / 1 - ----------------- *\/ polar_lift(1 - y) 24*x* / 1 - ----------------- *polar_lift (1 - y) 3/2 3 2 3/2 ___________________ 2 ___________________ 8*x* / 1 - ----------------- *\/ polar_lift(1 - y) 8*y* / 1 - ----------------- *polar_lift (1 - y) 18*x * / 1 - ----------------- *\/ polar_lift(1 - y) 60*y* / 1 - ----------------- *polar_lift (1 - y) 120*x* / 1 - ----------------- *polar_lift (1 - y) 180*x * / 1 - ----------------- *polar_lift (1 - y) 120*x*y* / 1 - ----------------- *polar_lift (1 - y) 8*x*y* / 1 - ----------------- *\/ polar_lift(1 - y) ___________________ 2 60*y*x * / 1 - ----------------- *\/ polar_lift(1 - y) |
| | | |4*polar_lift (1 - y) 60*polar_lift (1 - y) 60*x*polar_lift (1 - y) 60*y*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 3*x*polar_lift (1 - y) 3*x 2*x 2*y*polar_lift (1 - y) 4*x*\/ polar_lift(1 - y) 6*x *\/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 4*x*y*\/ polar_lift(1 - y) 2*y*x \/ polar_lift(1 - y) |
| | | y*|---------------------- + ----------------------- - ------------------------- - ------------------------- - --------------------------------------------------- - -------------------------------------------------- - ----------------------------------------------- + -------------------------------------------------- - ----------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------- - --------------------------------------------------------------------- - --------------------------------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------------- + ---------------------------------------------------- + ------------------------------------------------------- + ----------------------------------------------------- + ------------------------------------------------------ + ------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------- + --------------------------------------------------------------------- + ---------------------------------------------------------| otherwise
| | | | -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y _______________________ -15 + 15*x + 15*y 2 2 2 -15 + 15*x + 15*y _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ -15 + 15*x + 15*y -15 + 15*x + 15*y -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y _______________________ _______________________ 2 |
| | | | (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x ___________________ / x ___________________ / x / x / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x ___________________ (-15 + 15*x + 15*y) |
| | | | / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) |
| | \ \ \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) /
| |
| /
| 1 - y
<
| 1 - y
| /
| |
| | / / ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ \
| | | | / x 5/2 / x 3/2 / x 5/2 / x 5/2 3 / x ___________________ 2 / x ___________________ / x 3/2 / x ___________________ / x 3/2 2 / x ___________________ / x 5/2 / x 3/2 2 / x 3/2 / x 3/2 / x ___________________ 2 / x ___________________|
| | | | 5/2 5/2 5/2 5/2 60*I* / -1 + ----------------- *polar_lift (1 - y) 8*I* / -1 + ----------------- *polar_lift (1 - y) 3/2 6*I* / -1 + ----------------- *polar_lift (1 - y) 90*I*x* / -1 + ----------------- *polar_lift (1 - y) 90*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 60*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 24*I*x* / -1 + ----------------- *polar_lift (1 - y) 2 ___________________ ___________________ 3/2 2 3/2 3 8*I*x* / -1 + ----------------- *\/ polar_lift(1 - y) 8*I*y* / -1 + ----------------- *polar_lift (1 - y) 18*I*x * / -1 + ----------------- *\/ polar_lift(1 - y) 60*I*y* / -1 + ----------------- *polar_lift (1 - y) 120*I*x* / -1 + ----------------- *polar_lift (1 - y) 180*I*x * / -1 + ----------------- *polar_lift (1 - y) 120*I*x*y* / -1 + ----------------- *polar_lift (1 - y) 8*I*x*y* / -1 + ----------------- *\/ polar_lift(1 - y) 2 ___________________ 60*I*y*x * / -1 + ----------------- *\/ polar_lift(1 - y) |
| | | |4*polar_lift (1 - y) 60*polar_lift (1 - y) 60*x*polar_lift (1 - y) 60*y*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*I*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 6*I*x *\/ polar_lift(1 - y) 4*I*x*\/ polar_lift(1 - y) 2*I*y*polar_lift (1 - y) 2*I*x 3*I*x*polar_lift (1 - y) 3*I*x \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*I*y*x 4*I*x*y*\/ polar_lift(1 - y) \/ polar_lift(1 - y) | | x |
| | |y*|---------------------- + ----------------------- - ------------------------- - ------------------------- - ------------------------------------------------------ - ----------------------------------------------------- + ------------------------------------------------ + ----------------------------------------------------- - -------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------ - ------------------------------------------------ - ------------------------------------------------ + ---------------------------------------------------------------------- + ------------------------------------------------ + ---------------------------------------------------------------------- + -------------------------------------------------------- + ------------------------------------------------------- + ---------------------------------------------------------- + -------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------- - ----------------------------------------------------------- - ---------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------ + ------------------------------------------------------------| for |------| > 1
| | | | -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y ________________________ -15 + 15*x + 15*y 2 2 2 -15 + 15*x + 15*y ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ -15 + 15*x + 15*y -15 + 15*x + 15*y -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y ________________________ ________________________ 2 | |-1 + y|
| | | | (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x / x / x ___________________ / x / x ___________________ (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x ___________________ / x (-15 + 15*x + 15*y) |
| | | | / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / -1 + ----------------- *(-15 + 15*x + 15*y) |
| | | \ \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) /
| | < dx otherwise
| | | / _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ \
| | | | / x 5/2 / x 3/2 / x 5/2 / x 5/2 3 / x ___________________ 2 / x ___________________ / x 3/2 / x ___________________ / x 3/2 2 / x ___________________ / x 5/2 / x 3/2 2 / x 3/2 / x 3/2 / x ___________________ 2 / x ___________________|
| | | | 5/2 5/2 5/2 5/2 60* / 1 - ----------------- *polar_lift (1 - y) 8* / 1 - ----------------- *polar_lift (1 - y) 3/2 6* / 1 - ----------------- *polar_lift (1 - y) 90*x* / 1 - ----------------- *polar_lift (1 - y) 90*x * / 1 - ----------------- *\/ polar_lift(1 - y) 60*x * / 1 - ----------------- *\/ polar_lift(1 - y) 24*x* / 1 - ----------------- *polar_lift (1 - y) 3/2 3 2 3/2 ___________________ 2 ___________________ 8*x* / 1 - ----------------- *\/ polar_lift(1 - y) 8*y* / 1 - ----------------- *polar_lift (1 - y) 18*x * / 1 - ----------------- *\/ polar_lift(1 - y) 60*y* / 1 - ----------------- *polar_lift (1 - y) 120*x* / 1 - ----------------- *polar_lift (1 - y) 180*x * / 1 - ----------------- *polar_lift (1 - y) 120*x*y* / 1 - ----------------- *polar_lift (1 - y) 8*x*y* / 1 - ----------------- *\/ polar_lift(1 - y) ___________________ 2 60*y*x * / 1 - ----------------- *\/ polar_lift(1 - y) |
| | | |4*polar_lift (1 - y) 60*polar_lift (1 - y) 60*x*polar_lift (1 - y) 60*y*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 2*polar_lift (1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 3*x*polar_lift (1 - y) 3*x 2*x 2*y*polar_lift (1 - y) 4*x*\/ polar_lift(1 - y) 6*x *\/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) 4*x*y*\/ polar_lift(1 - y) 2*y*x \/ polar_lift(1 - y) |
| | | y*|---------------------- + ----------------------- - ------------------------- - ------------------------- - --------------------------------------------------- - -------------------------------------------------- - ----------------------------------------------- + -------------------------------------------------- - ----------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------- - --------------------------------------------------------------------- - --------------------------------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + ----------------------------------------------------- + ---------------------------------------------------- + ------------------------------------------------------- + ----------------------------------------------------- + ------------------------------------------------------ + ------------------------------------------------------- - -------------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------- + --------------------------------------------------------------------- + ---------------------------------------------------------| otherwise
| | | | -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y _______________________ -15 + 15*x + 15*y 2 2 2 -15 + 15*x + 15*y _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ -15 + 15*x + 15*y -15 + 15*x + 15*y -15 + 15*x + 15*y 2 2 2 2 -15 + 15*x + 15*y _______________________ _______________________ 2 |
| | | | (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x ___________________ / x ___________________ / x / x / x (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) (-15 + 15*x + 15*y) / x / x ___________________ (-15 + 15*x + 15*y) |
| | | | / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y) / 1 - ----------------- *(-15 + 15*x + 15*y)*\/ polar_lift(1 - y) |
| | \ \ \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) \/ polar_lift(1 - y) /
| |
| /
\ 0
⎩⎨⎧−1−y∫0⎩⎨⎧y(−(15x+15y−15)290ix3polar_lift(1−y)x−1polar_lift(1−y)+polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)3ix3+(15x+15y−15)260ix2ypolar_lift(1−y)x−1polar_lift(1−y)−polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)2ix2y+15x+15y−1518ix2polar_lift(1−y)x−1polar_lift(1−y)+(15x+15y−15)2180ix2polar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260ix2polar_lift(1−y)x−1polar_lift(1−y)−polar_lift(1−y)x−1(15x+15y−15)6ix2polar_lift(1−y)+polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)2ix2−15x+15y−158ixypolar_lift(1−y)x−1polar_lift(1−y)−(15x+15y−15)2120ixypolar_lift(1−y)x−1polar_lift23(1−y)+polar_lift(1−y)x−1(15x+15y−15)4ixypolar_lift(1−y)−15x+15y−1524ixpolar_lift(1−y)x−1polar_lift23(1−y)+15x+15y−158ixpolar_lift(1−y)x−1polar_lift(1−y)−(15x+15y−15)290ixpolar_lift(1−y)x−1polar_lift25(1−y)+(15x+15y−15)2120ixpolar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260xpolar_lift25(1−y)+polar_lift(1−y)x−1(15x+15y−15)3ixpolar_lift23(1−y)−polar_lift(1−y)x−1(15x+15y−15)4ixpolar_lift(1−y)+15x+15y−158iypolar_lift(1−y)x−1polar_lift23(1−y)+(15x+15y−15)260iypolar_lift(1−y)x−1polar_lift25(1−y)−(15x+15y−15)260ypolar_lift25(1−y)−polar_lift(1−y)x−1(15x+15y−15)2iypolar_lift23(1−y)+15x+15y−156ipolar_lift(1−y)x−1polar_lift25(1−y)−15x+15y−158ipolar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260ipolar_lift(1−y)x−1polar_lift25(1−y)+15x+15y−154polar_lift25(1−y)+(15x+15y−15)260polar_lift25(1−y)+polar_lift(1−y)x−1(15x+15y−15)2ipolar_lift23(1−y))y(−(15x+15y−15)290x3−polar_lift(1−y)x+1polar_lift(1−y)−−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)3x3+(15x+15y−15)260x2y−polar_lift(1−y)x+1polar_lift(1−y)+−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)2x2y+15x+15y−1518x2−polar_lift(1−y)x+1polar_lift(1−y)+(15x+15y−15)2180x2−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260x2−polar_lift(1−y)x+1polar_lift(1−y)+−polar_lift(1−y)x+1(15x+15y−15)6x2polar_lift(1−y)−−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)2x2−15x+15y−158xy−polar_lift(1−y)x+1polar_lift(1−y)−(15x+15y−15)2120xy−polar_lift(1−y)x+1polar_lift23(1−y)−−polar_lift(1−y)x+1(15x+15y−15)4xypolar_lift(1−y)−15x+15y−1524x−polar_lift(1−y)x+1polar_lift23(1−y)+15x+15y−158x−polar_lift(1−y)x+1polar_lift(1−y)−(15x+15y−15)290x−polar_lift(1−y)x+1polar_lift25(1−y)+(15x+15y−15)2120x−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260xpolar_lift25(1−y)−−polar_lift(1−y)x+1(15x+15y−15)3xpolar_lift23(1−y)+−polar_lift(1−y)x+1(15x+15y−15)4xpolar_lift(1−y)+15x+15y−158y−polar_lift(1−y)x+1polar_lift23(1−y)+(15x+15y−15)260y−polar_lift(1−y)x+1polar_lift25(1−y)−(15x+15y−15)260ypolar_lift25(1−y)+−polar_lift(1−y)x+1(15x+15y−15)2ypolar_lift23(1−y)+15x+15y−156−polar_lift(1−y)x+1polar_lift25(1−y)−15x+15y−158−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260−polar_lift(1−y)x+1polar_lift25(1−y)+15x+15y−154polar_lift25(1−y)+(15x+15y−15)260polar_lift25(1−y)−−polar_lift(1−y)x+1(15x+15y−15)2polar_lift23(1−y))fory−1x>1otherwisedx0∫1−y⎩⎨⎧y(−(15x+15y−15)290ix3polar_lift(1−y)x−1polar_lift(1−y)+polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)3ix3+(15x+15y−15)260ix2ypolar_lift(1−y)x−1polar_lift(1−y)−polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)2ix2y+15x+15y−1518ix2polar_lift(1−y)x−1polar_lift(1−y)+(15x+15y−15)2180ix2polar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260ix2polar_lift(1−y)x−1polar_lift(1−y)−polar_lift(1−y)x−1(15x+15y−15)6ix2polar_lift(1−y)+polar_lift(1−y)x−1(15x+15y−15)polar_lift(1−y)2ix2−15x+15y−158ixypolar_lift(1−y)x−1polar_lift(1−y)−(15x+15y−15)2120ixypolar_lift(1−y)x−1polar_lift23(1−y)+polar_lift(1−y)x−1(15x+15y−15)4ixypolar_lift(1−y)−15x+15y−1524ixpolar_lift(1−y)x−1polar_lift23(1−y)+15x+15y−158ixpolar_lift(1−y)x−1polar_lift(1−y)−(15x+15y−15)290ixpolar_lift(1−y)x−1polar_lift25(1−y)+(15x+15y−15)2120ixpolar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260xpolar_lift25(1−y)+polar_lift(1−y)x−1(15x+15y−15)3ixpolar_lift23(1−y)−polar_lift(1−y)x−1(15x+15y−15)4ixpolar_lift(1−y)+15x+15y−158iypolar_lift(1−y)x−1polar_lift23(1−y)+(15x+15y−15)260iypolar_lift(1−y)x−1polar_lift25(1−y)−(15x+15y−15)260ypolar_lift25(1−y)−polar_lift(1−y)x−1(15x+15y−15)2iypolar_lift23(1−y)+15x+15y−156ipolar_lift(1−y)x−1polar_lift25(1−y)−15x+15y−158ipolar_lift(1−y)x−1polar_lift23(1−y)−(15x+15y−15)260ipolar_lift(1−y)x−1polar_lift25(1−y)+15x+15y−154polar_lift25(1−y)+(15x+15y−15)260polar_lift25(1−y)+polar_lift(1−y)x−1(15x+15y−15)2ipolar_lift23(1−y))y(−(15x+15y−15)290x3−polar_lift(1−y)x+1polar_lift(1−y)−−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)3x3+(15x+15y−15)260x2y−polar_lift(1−y)x+1polar_lift(1−y)+−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)2x2y+15x+15y−1518x2−polar_lift(1−y)x+1polar_lift(1−y)+(15x+15y−15)2180x2−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260x2−polar_lift(1−y)x+1polar_lift(1−y)+−polar_lift(1−y)x+1(15x+15y−15)6x2polar_lift(1−y)−−polar_lift(1−y)x+1(15x+15y−15)polar_lift(1−y)2x2−15x+15y−158xy−polar_lift(1−y)x+1polar_lift(1−y)−(15x+15y−15)2120xy−polar_lift(1−y)x+1polar_lift23(1−y)−−polar_lift(1−y)x+1(15x+15y−15)4xypolar_lift(1−y)−15x+15y−1524x−polar_lift(1−y)x+1polar_lift23(1−y)+15x+15y−158x−polar_lift(1−y)x+1polar_lift(1−y)−(15x+15y−15)290x−polar_lift(1−y)x+1polar_lift25(1−y)+(15x+15y−15)2120x−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260xpolar_lift25(1−y)−−polar_lift(1−y)x+1(15x+15y−15)3xpolar_lift23(1−y)+−polar_lift(1−y)x+1(15x+15y−15)4xpolar_lift(1−y)+15x+15y−158y−polar_lift(1−y)x+1polar_lift23(1−y)+(15x+15y−15)260y−polar_lift(1−y)x+1polar_lift25(1−y)−(15x+15y−15)260ypolar_lift25(1−y)+−polar_lift(1−y)x+1(15x+15y−15)2ypolar_lift23(1−y)+15x+15y−156−polar_lift(1−y)x+1polar_lift25(1−y)−15x+15y−158−polar_lift(1−y)x+1polar_lift23(1−y)−(15x+15y−15)260−polar_lift(1−y)x+1polar_lift25(1−y)+15x+15y−154polar_lift25(1−y)+(15x+15y−15)260polar_lift25(1−y)−−polar_lift(1−y)x+1(15x+15y−15)2polar_lift23(1−y))fory−1x>1otherwisedxfory−1>0otherwise
Piecewise((-Integral(Piecewise((y*(4*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y) + 60*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*x*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*y*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*i*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 8*i*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) + 2*i*polar_lift(1 - y)^(3/2)/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 6*i*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y) - 90*i*x*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 90*i*x^3*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2 - 60*i*x^2*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2 - 24*i*x*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) - 6*i*x^2*sqrt(polar_lift(1 - y))/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) - 4*i*x*sqrt(polar_lift(1 - y))/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) - 2*i*y*polar_lift(1 - y)^(3/2)/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 2*i*x^2/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 3*i*x*polar_lift(1 - y)^(3/2)/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 3*i*x^3/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 8*i*x*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) + 8*i*y*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) + 18*i*x^2*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) + 60*i*y*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 + 120*i*x*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 + 180*i*x^2*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 - 120*i*x*y*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 - 8*i*x*y*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) - 2*i*y*x^2/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 4*i*x*y*sqrt(polar_lift(1 - y))/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 60*i*y*x^2*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2), Abs(x/(-1 + y)) > 1), (y*(4*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y) + 60*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*x*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*y*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 8*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) - 2*polar_lift(1 - y)^(3/2)/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 6*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y) - 90*x*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 90*x^3*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2 - 60*x^2*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2 - 24*x*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) - 3*x*polar_lift(1 - y)^(3/2)/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) - 3*x^3/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) - 2*x^2/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 2*y*polar_lift(1 - y)^(3/2)/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 4*x*sqrt(polar_lift(1 - y))/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 6*x^2*sqrt(polar_lift(1 - y))/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 8*x*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) + 8*y*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) + 18*x^2*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) + 60*y*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 + 120*x*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 + 180*x^2*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 - 120*x*y*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 - 8*x*y*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) - 4*x*y*sqrt(polar_lift(1 - y))/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 2*y*x^2/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 60*y*x^2*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2), True)), (x, 1 - y, 0)), -1 + y > 0), (Integral(Piecewise((y*(4*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y) + 60*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*x*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*y*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*i*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 8*i*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) + 2*i*polar_lift(1 - y)^(3/2)/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 6*i*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y) - 90*i*x*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 90*i*x^3*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2 - 60*i*x^2*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2 - 24*i*x*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) - 6*i*x^2*sqrt(polar_lift(1 - y))/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) - 4*i*x*sqrt(polar_lift(1 - y))/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) - 2*i*y*polar_lift(1 - y)^(3/2)/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 2*i*x^2/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 3*i*x*polar_lift(1 - y)^(3/2)/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 3*i*x^3/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 8*i*x*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) + 8*i*y*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) + 18*i*x^2*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) + 60*i*y*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 + 120*i*x*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 + 180*i*x^2*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 - 120*i*x*y*sqrt(-1 + x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 - 8*i*x*y*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) - 2*i*y*x^2/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 4*i*x*y*sqrt(polar_lift(1 - y))/(sqrt(-1 + x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 60*i*y*x^2*sqrt(-1 + x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2), Abs(x/(-1 + y)) > 1), (y*(4*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y) + 60*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*x*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*y*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 60*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 8*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) - 2*polar_lift(1 - y)^(3/2)/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 6*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y) - 90*x*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 - 90*x^3*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2 - 60*x^2*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2 - 24*x*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) - 3*x*polar_lift(1 - y)^(3/2)/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) - 3*x^3/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) - 2*x^2/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 2*y*polar_lift(1 - y)^(3/2)/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 4*x*sqrt(polar_lift(1 - y))/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 6*x^2*sqrt(polar_lift(1 - y))/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 8*x*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) + 8*y*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y) + 18*x^2*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) + 60*y*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(5/2)/(-15 + 15*x + 15*y)^2 + 120*x*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 + 180*x^2*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 - 120*x*y*sqrt(1 - x/polar_lift(1 - y))*polar_lift(1 - y)^(3/2)/(-15 + 15*x + 15*y)^2 - 8*x*y*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y) - 4*x*y*sqrt(polar_lift(1 - y))/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)) + 2*y*x^2/(sqrt(1 - x/polar_lift(1 - y))*(-15 + 15*x + 15*y)*sqrt(polar_lift(1 - y))) + 60*y*x^2*sqrt(1 - x/polar_lift(1 - y))*sqrt(polar_lift(1 - y))/(-15 + 15*x + 15*y)^2), True)), (x, 0, 1 - y)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.
