3.2406 \(\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^9} \, dx\)

Optimal. Leaf size=267 \[ \frac{47365 \sqrt{1-2 x} (5 x+3)^{5/2}}{36288 (3 x+2)^6}+\frac{185 (1-2 x)^{3/2} (5 x+3)^{5/2}}{1008 (3 x+2)^7}-\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{24 (3 x+2)^8}-\frac{720833 \sqrt{1-2 x} (5 x+3)^{3/2}}{508032 (3 x+2)^5}+\frac{6796051494355 \sqrt{1-2 x} \sqrt{5 x+3}}{200741732352 (3 x+2)}+\frac{64983635965 \sqrt{1-2 x} \sqrt{5 x+3}}{14338695168 (3 x+2)^2}+\frac{372439373 \sqrt{1-2 x} \sqrt{5 x+3}}{512096256 (3 x+2)^3}-\frac{75045071 \sqrt{1-2 x} \sqrt{5 x+3}}{85349376 (3 x+2)^4}-\frac{106656830005 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{275365888 \sqrt{7}} \]

[Out]

(-75045071*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(85349376*(2 + 3*x)^4) + (372439373*Sqrt
[1 - 2*x]*Sqrt[3 + 5*x])/(512096256*(2 + 3*x)^3) + (64983635965*Sqrt[1 - 2*x]*Sq
rt[3 + 5*x])/(14338695168*(2 + 3*x)^2) + (6796051494355*Sqrt[1 - 2*x]*Sqrt[3 + 5
*x])/(200741732352*(2 + 3*x)) - (720833*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(508032*(
2 + 3*x)^5) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(24*(2 + 3*x)^8) + (185*(1 - 2*x
)^(3/2)*(3 + 5*x)^(5/2))/(1008*(2 + 3*x)^7) + (47365*Sqrt[1 - 2*x]*(3 + 5*x)^(5/
2))/(36288*(2 + 3*x)^6) - (106656830005*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5
*x])])/(275365888*Sqrt[7])

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Rubi [A]  time = 0.627345, antiderivative size = 267, normalized size of antiderivative = 1., number of steps used = 11, number of rules used = 6, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{47365 \sqrt{1-2 x} (5 x+3)^{5/2}}{36288 (3 x+2)^6}+\frac{185 (1-2 x)^{3/2} (5 x+3)^{5/2}}{1008 (3 x+2)^7}-\frac{(1-2 x)^{5/2} (5 x+3)^{5/2}}{24 (3 x+2)^8}-\frac{720833 \sqrt{1-2 x} (5 x+3)^{3/2}}{508032 (3 x+2)^5}+\frac{6796051494355 \sqrt{1-2 x} \sqrt{5 x+3}}{200741732352 (3 x+2)}+\frac{64983635965 \sqrt{1-2 x} \sqrt{5 x+3}}{14338695168 (3 x+2)^2}+\frac{372439373 \sqrt{1-2 x} \sqrt{5 x+3}}{512096256 (3 x+2)^3}-\frac{75045071 \sqrt{1-2 x} \sqrt{5 x+3}}{85349376 (3 x+2)^4}-\frac{106656830005 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{275365888 \sqrt{7}} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^9,x]

[Out]

(-75045071*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(85349376*(2 + 3*x)^4) + (372439373*Sqrt
[1 - 2*x]*Sqrt[3 + 5*x])/(512096256*(2 + 3*x)^3) + (64983635965*Sqrt[1 - 2*x]*Sq
rt[3 + 5*x])/(14338695168*(2 + 3*x)^2) + (6796051494355*Sqrt[1 - 2*x]*Sqrt[3 + 5
*x])/(200741732352*(2 + 3*x)) - (720833*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(508032*(
2 + 3*x)^5) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(24*(2 + 3*x)^8) + (185*(1 - 2*x
)^(3/2)*(3 + 5*x)^(5/2))/(1008*(2 + 3*x)^7) + (47365*Sqrt[1 - 2*x]*(3 + 5*x)^(5/
2))/(36288*(2 + 3*x)^6) - (106656830005*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5
*x])])/(275365888*Sqrt[7])

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Rubi in Sympy [A]  time = 60.6948, size = 245, normalized size = 0.92 \[ - \frac{25895 \left (- 2 x + 1\right )^{\frac{5}{2}} \sqrt{5 x + 3}}{1778112 \left (3 x + 2\right )^{6}} - \frac{185 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (5 x + 3\right )^{\frac{3}{2}}}{7056 \left (3 x + 2\right )^{7}} - \frac{\left (- 2 x + 1\right )^{\frac{5}{2}} \left (5 x + 3\right )^{\frac{5}{2}}}{24 \left (3 x + 2\right )^{8}} + \frac{11833 \left (- 2 x + 1\right )^{\frac{3}{2}} \sqrt{5 x + 3}}{169344 \left (3 x + 2\right )^{5}} + \frac{6796051494355 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{200741732352 \left (3 x + 2\right )} + \frac{64983635965 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{14338695168 \left (3 x + 2\right )^{2}} + \frac{372439373 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{512096256 \left (3 x + 2\right )^{3}} + \frac{1392991 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{12192768 \left (3 x + 2\right )^{4}} - \frac{106656830005 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{1927561216} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**(5/2)*(3+5*x)**(5/2)/(2+3*x)**9,x)

[Out]

-25895*(-2*x + 1)**(5/2)*sqrt(5*x + 3)/(1778112*(3*x + 2)**6) - 185*(-2*x + 1)**
(5/2)*(5*x + 3)**(3/2)/(7056*(3*x + 2)**7) - (-2*x + 1)**(5/2)*(5*x + 3)**(5/2)/
(24*(3*x + 2)**8) + 11833*(-2*x + 1)**(3/2)*sqrt(5*x + 3)/(169344*(3*x + 2)**5)
+ 6796051494355*sqrt(-2*x + 1)*sqrt(5*x + 3)/(200741732352*(3*x + 2)) + 64983635
965*sqrt(-2*x + 1)*sqrt(5*x + 3)/(14338695168*(3*x + 2)**2) + 372439373*sqrt(-2*
x + 1)*sqrt(5*x + 3)/(512096256*(3*x + 2)**3) + 1392991*sqrt(-2*x + 1)*sqrt(5*x
+ 3)/(12192768*(3*x + 2)**4) - 106656830005*sqrt(7)*atan(sqrt(7)*sqrt(-2*x + 1)/
(7*sqrt(5*x + 3)))/1927561216

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Mathematica [A]  time = 0.163766, size = 102, normalized size = 0.38 \[ \frac{\frac{14 \sqrt{1-2 x} \sqrt{5 x+3} \left (61164463449195 x^7+288163475473440 x^6+581931572602156 x^5+652979564561296 x^4+439702534402320 x^3+177688060285568 x^2+39899303549504 x+3840133416192\right )}{(3 x+2)^8}-319970490015 \sqrt{7} \tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{11565367296} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^9,x]

[Out]

((14*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(3840133416192 + 39899303549504*x + 17768806028
5568*x^2 + 439702534402320*x^3 + 652979564561296*x^4 + 581931572602156*x^5 + 288
163475473440*x^6 + 61164463449195*x^7))/(2 + 3*x)^8 - 319970490015*Sqrt[7]*ArcTa
n[(-20 - 37*x)/(2*Sqrt[7 - 14*x]*Sqrt[3 + 5*x])])/11565367296

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Maple [B]  time = 0.037, size = 442, normalized size = 1.7 \[{\frac{1}{11565367296\, \left ( 2+3\,x \right ) ^{8}}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 2099326384988415\,\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) \sqrt{7}{x}^{8}+11196407386604880\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{7}+26124950568744720\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{6}[phone]\,{x}^{7}\sqrt{-10\,{x}^{2}-x+3}+34833267424992960\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{5}+4034288656628160\,{x}^{6}\sqrt{-10\,{x}^{2}-x+3}+29027722854160800\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{4}+8147042016430184\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}+15481452188885760\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{3}+9141713903858144\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}+5160484062961920\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{2}+6155835481632480\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) x+2487632843997952\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) [phone]\,x\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^9,x)

[Out]

1/11565367296*(1-2*x)^(1/2)*(3+5*x)^(1/2)*(2099326384988415*arctan(1/14*(37*x+20
)*7^(1/2)/(-10*x^2-x+3)^(1/2))*7^(1/2)*x^8+11196407386604880*7^(1/2)*arctan(1/14
*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^7+26124950568744720*7^(1/2)*arctan(1/1
4*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^6+856302488288730*x^7*(-10*x^2-x+3)^(
1/2)+34833267424992960*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2)
)*x^5+4034288656628160*x^6*(-10*x^2-x+3)^(1/2)+29027722854160800*7^(1/2)*arctan(
1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^4+8147042016430184*x^5*(-10*x^2-x+
3)^(1/2)+15481452188885760*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(
1/2))*x^3+9141713903858144*x^4*(-10*x^2-x+3)^(1/2)+5160484062961920*7^(1/2)*arct
an(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^2+6155835481632480*x^3*(-10*x^2
-x+3)^(1/2)[phone]*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^
(1/2))*x+2487632843997952*x^2*(-10*x^2-x+3)^(1/2)[phone]*7^(1/2)*arctan(
1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))[phone]*x*(-10*x^2-x+3)^(1/2
)[phone]*(-10*x^2-x+3)^(1/2))/(-10*x^2-x+3)^(1/2)/(2+3*x)^8

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Maxima [A]  time = 1.53103, size = 552, normalized size = 2.07 \[ \frac{39793036595}{30359089152} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}} + \frac{3 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{56 \,{\left (6561 \, x^{8} + 34992 \, x^{7} + 81648 \, x^{6} + 108864 \, x^{5} + 90720 \, x^{4} + 48384 \, x^{3} + 16128 \, x^{2} + 3072 \, x + 256\right )}} + \frac{999 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{5488 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + \frac{12041 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{21952 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{445517 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{307328 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{52823867 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{17210368 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{984147053 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{240945152 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{7958607319 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{6746464256 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{712927441325}{20239392768} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x + \frac{1368574460935}{40478785536} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} - \frac{1321083986311 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{121436356608 \,{\left (3 \, x + 2\right )}} + \frac{163070359925}{963780608} \, \sqrt{-10 \, x^{2} - x + 3} x + \frac{106656830005}{3855122432} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) - \frac{143678209015}{1927561216} \, \sqrt{-10 \, x^{2} - x + 3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^(5/2)*(-2*x + 1)^(5/2)/(3*x + 2)^9,x, algorithm="maxima")

[Out]

39793036595/30359089152*(-10*x^2 - x + 3)^(5/2) + 3/56*(-10*x^2 - x + 3)^(7/2)/(
6561*x^8 + 34992*x^7 + 81648*x^6 + 108864*x^5 + 90720*x^4 + 48384*x^3 + 16128*x^
2 + 3072*x + 256) + 999/5488*(-10*x^2 - x + 3)^(7/2)/(2187*x^7 + 10206*x^6 + 204
12*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128) + 12041/21952*(-10*x^2
- x + 3)^(7/2)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 6
4) + 445517/307328*(-10*x^2 - x + 3)^(7/2)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x
^2 + 240*x + 32) + 52823867/17210368*(-10*x^2 - x + 3)^(7/2)/(81*x^4 + 216*x^3 +
216*x^2 + 96*x + 16) + 984147053/240945152*(-10*x^2 - x + 3)^(7/2)/(27*x^3 + 54
*x^2 + 36*x + 8) + 7958607319/6746464256*(-10*x^2 - x + 3)^(7/2)/(9*x^2 + 12*x +
4) - 712927441325/20239392768*(-10*x^2 - x + 3)^(3/2)*x + 1368574460935/4047878
5536*(-10*x^2 - x + 3)^(3/2) - 1321083986311/121436356608*(-10*x^2 - x + 3)^(5/2
)/(3*x + 2) + 163070359925/963780608*sqrt(-10*x^2 - x + 3)*x + 106656830005/3855
122432*sqrt(7)*arcsin(37/11*x/abs(3*x + 2) + 20/11/abs(3*x + 2)) - 143678209015/
1927561216*sqrt(-10*x^2 - x + 3)

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Fricas [A]  time = 0.231125, size = 228, normalized size = 0.85 \[ \frac{\sqrt{7}{\left (2 \, \sqrt{7}{\left (61164463449195 \, x^{7} + 288163475473440 \, x^{6} + 581931572602156 \, x^{5} + 652979564561296 \, x^{4} + 439702534402320 \, x^{3} + 177688060285568 \, x^{2} + 39899303549504 \, x + 3840133416192\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 319970490015 \,{\left (6561 \, x^{8} + 34992 \, x^{7} + 81648 \, x^{6} + 108864 \, x^{5} + 90720 \, x^{4} + 48384 \, x^{3} + 16128 \, x^{2} + 3072 \, x + 256\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{11565367296 \,{\left (6561 \, x^{8} + 34992 \, x^{7} + 81648 \, x^{6} + 108864 \, x^{5} + 90720 \, x^{4} + 48384 \, x^{3} + 16128 \, x^{2} + 3072 \, x + 256\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^(5/2)*(-2*x + 1)^(5/2)/(3*x + 2)^9,x, algorithm="fricas")

[Out]

1/11565367296*sqrt(7)*(2*sqrt(7)*(61164463449195*x^7 + 288163475473440*x^6 + 581
931572602156*x^5 + 652979564561296*x^4 + 439702534402320*x^3 + 177688060285568*x
^2 + 39899303549504*x + 3840133416192)*sqrt(5*x + 3)*sqrt(-2*x + 1) + 3199704900
15*(6561*x^8 + 34992*x^7 + 81648*x^6 + 108864*x^5 + 90720*x^4 + 48384*x^3 + 1612
8*x^2 + 3072*x + 256)*arctan(1/14*sqrt(7)*(37*x + 20)/(sqrt(5*x + 3)*sqrt(-2*x +
1))))/(6561*x^8 + 34992*x^7 + 81648*x^6 + 108864*x^5 + 90720*x^4 + 48384*x^3 +
16128*x^2 + 3072*x + 256)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**(5/2)*(3+5*x)**(5/2)/(2+3*x)**9,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.942972, size = 841, normalized size = 3.15 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^(5/2)*(-2*x + 1)^(5/2)/(3*x + 2)^9,x, algorithm="giac")

[Out]

21331366001/7710244864*sqrt(70)*sqrt(10)*(pi + 2*arctan(-1/140*sqrt(70)*sqrt(5*x
+ 3)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))^2/(5*x + 3) - 4)/(sqrt(2)*sqrt(-10*x
+ 5) - sqrt(22)))) - 8857805/413048832*(36123*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5
) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22
)))^15 + 77544040*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) -
4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^13 + 72311503040*sqrt(10)
*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*
sqrt(-10*x + 5) - sqrt(22)))^11 - 37368091174400*sqrt(10)*((sqrt(2)*sqrt(-10*x +
5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(
22)))^9 - 10615979648512000*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(
5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^7 - 15873821147
34080000*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5
*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^5 - 133456146460672000000*sqrt(10)
*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*
sqrt(-10*x + 5) - sqrt(22)))^3 - 4874050566389760000000*sqrt(10)*((sqrt(2)*sqrt(
-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5)
- sqrt(22))))/(((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x
+ 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^2 + 280)^8