3.2405 \(\int \frac{(1-2 x)^{5/2} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=238 \[ \frac{4477 \sqrt{1-2 x} (5 x+3)^{7/2}}{448 (3 x+2)^4}+\frac{407 (1-2 x)^{3/2} (5 x+3)^{7/2}}{168 (3 x+2)^5}+\frac{37 (1-2 x)^{5/2} (5 x+3)^{7/2}}{84 (3 x+2)^6}+\frac{3 (1-2 x)^{7/2} (5 x+3)^{7/2}}{49 (3 x+2)^7}-\frac{49247 \sqrt{1-2 x} (5 x+3)^{5/2}}{18816 (3 x+2)^3}-\frac{2708585 \sqrt{1-2 x} (5 x+3)^{3/2}}{526848 (3 x+2)^2}-\frac{29794435 \sqrt{1-2 x} \sqrt{5 x+3}}{2458624 (3 x+2)}-\frac{327738785 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{2458624 \sqrt{7}} \]

[Out]

(-29794435*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2458624*(2 + 3*x)) - (2708585*Sqrt[1 -
2*x]*(3 + 5*x)^(3/2))/(526848*(2 + 3*x)^2) - (49247*Sqrt[1 - 2*x]*(3 + 5*x)^(5/2
))/(18816*(2 + 3*x)^3) + (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/(49*(2 + 3*x)^7) +
(37*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(84*(2 + 3*x)^6) + (407*(1 - 2*x)^(3/2)*(3
+ 5*x)^(7/2))/(168*(2 + 3*x)^5) + (4477*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2))/(448*(2 +
3*x)^4) - (327738785*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(2458624*Sq
rt[7])

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Rubi [A]  time = 0.37682, antiderivative size = 238, normalized size of antiderivative = 1., number of steps used = 9, number of rules used = 4, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{4477 \sqrt{1-2 x} (5 x+3)^{7/2}}{448 (3 x+2)^4}+\frac{407 (1-2 x)^{3/2} (5 x+3)^{7/2}}{168 (3 x+2)^5}+\frac{37 (1-2 x)^{5/2} (5 x+3)^{7/2}}{84 (3 x+2)^6}+\frac{3 (1-2 x)^{7/2} (5 x+3)^{7/2}}{49 (3 x+2)^7}-\frac{49247 \sqrt{1-2 x} (5 x+3)^{5/2}}{18816 (3 x+2)^3}-\frac{2708585 \sqrt{1-2 x} (5 x+3)^{3/2}}{526848 (3 x+2)^2}-\frac{29794435 \sqrt{1-2 x} \sqrt{5 x+3}}{2458624 (3 x+2)}-\frac{327738785 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{2458624 \sqrt{7}} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^8,x]

[Out]

(-29794435*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(2458624*(2 + 3*x)) - (2708585*Sqrt[1 -
2*x]*(3 + 5*x)^(3/2))/(526848*(2 + 3*x)^2) - (49247*Sqrt[1 - 2*x]*(3 + 5*x)^(5/2
))/(18816*(2 + 3*x)^3) + (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/(49*(2 + 3*x)^7) +
(37*(1 - 2*x)^(5/2)*(3 + 5*x)^(7/2))/(84*(2 + 3*x)^6) + (407*(1 - 2*x)^(3/2)*(3
+ 5*x)^(7/2))/(168*(2 + 3*x)^5) + (4477*Sqrt[1 - 2*x]*(3 + 5*x)^(7/2))/(448*(2 +
3*x)^4) - (327738785*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(2458624*Sq
rt[7])

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Rubi in Sympy [A]  time = 28.4469, size = 219, normalized size = 0.92 \[ - \frac{407 \left (- 2 x + 1\right )^{\frac{7}{2}} \left (5 x + 3\right )^{\frac{3}{2}}}{8232 \left (3 x + 2\right )^{5}} - \frac{37 \left (- 2 x + 1\right )^{\frac{7}{2}} \left (5 x + 3\right )^{\frac{5}{2}}}{588 \left (3 x + 2\right )^{6}} + \frac{3 \left (- 2 x + 1\right )^{\frac{7}{2}} \left (5 x + 3\right )^{\frac{7}{2}}}{49 \left (3 x + 2\right )^{7}} - \frac{246235 \left (- 2 x + 1\right )^{\frac{5}{2}} \sqrt{5 x + 3}}{921984 \left (3 x + 2\right )^{3}} + \frac{4477 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (5 x + 3\right )^{\frac{3}{2}}}{21952 \left (3 x + 2\right )^{4}} + \frac{2708585 \left (- 2 x + 1\right )^{\frac{3}{2}} \sqrt{5 x + 3}}{3687936 \left (3 x + 2\right )^{2}} + \frac{29794435 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{2458624 \left (3 x + 2\right )} - \frac{327738785 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{17210368} \]

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)**8,x)

[Out]

-407*(-2*x + 1)**(7/2)*(5*x + 3)**(3/2)/(8232*(3*x + 2)**5) - 37*(-2*x + 1)**(7/
2)*(5*x + 3)**(5/2)/(588*(3*x + 2)**6) + 3*(-2*x + 1)**(7/2)*(5*x + 3)**(7/2)/(4
9*(3*x + 2)**7) - 246235*(-2*x + 1)**(5/2)*sqrt(5*x + 3)/(921984*(3*x + 2)**3) +
4477*(-2*x + 1)**(5/2)*(5*x + 3)**(3/2)/(21952*(3*x + 2)**4) + 2708585*(-2*x +
1)**(3/2)*sqrt(5*x + 3)/(3687936*(3*x + 2)**2) + 29794435*sqrt(-2*x + 1)*sqrt(5*
x + 3)/(2458624*(3*x + 2)) - 327738785*sqrt(7)*atan(sqrt(7)*sqrt(-2*x + 1)/(7*sq
rt(5*x + 3)))/17210368

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Mathematica [A]  time = 0.153851, size = 97, normalized size = 0.41 \[ \frac{\frac{14 \sqrt{1-2 x} \sqrt{5 x+3} \left (62659925205 x^6+253441751890 x^5+427105196104 x^4+384048502848 x^3+194338741616 x^2+52456780256 x+5897927808\right )}{(3 x+2)^7}-983216355 \sqrt{7} \tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{103262208} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2))/(2 + 3*x)^8,x]

[Out]

((14*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(5897927808 + 52456780256*x + 194338741616*x^2
+ 384048502848*x^3 + 427105196104*x^4 + 253441751890*x^5 + 62659925205*x^6))/(2
+ 3*x)^7 - 983216355*Sqrt[7]*ArcTan[(-20 - 37*x)/(2*Sqrt[7 - 14*x]*Sqrt[3 + 5*x]
)])/103262208

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Maple [B]  time = 0.019, size = 394, normalized size = 1.7 \[{\frac{1}{103262208\, \left ( 2+3\,x \right ) ^{7}}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 2150294168385\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{7}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{6}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{5}[phone]\,{x}^{6}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{4}[phone]\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{3}[phone]\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{2}[phone]\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) x+2720742382624\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) [phone]\,x\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]

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)^8,x)

[Out]

1/103262208*(1-2*x)^(1/2)*(3+5*x)^(1/2)*(2150294168385*7^(1/2)*arctan(1/14*(37*x
+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^7+10034706119130*7^(1/2)*arctan(1/14*(37*x+2
0)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^6+20069412238260*7^(1/2)*arctan(1/14*(37*x+20)
*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^5+877238952870*x^6*(-10*x^2-x+3)^(1/2)[phone]
31400*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^4+35481845264
60*x^5*(-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^3+5979472745456*x^4*(-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^2+5376679039872*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+2720742382624*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)+82
570989312*(-10*x^2-x+3)^(1/2))/(-10*x^2-x+3)^(1/2)/(2+3*x)^7

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Maxima [A]  time = 1.52865, size = 477, normalized size = 2. \[ \frac{122277415}{271063296} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}} + \frac{3 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{49 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + \frac{37 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{196 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{1369 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{2744 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{162319 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{153664 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{3024121 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{2151296 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{24455483 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{7}{2}}}{60236288 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{2190708025}{180708864} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x + \frac{4205402795}{361417728} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} - \frac{4059472427 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{1084253184 \,{\left (3 \, x + 2\right )}} + \frac{501088225}{8605184} \, \sqrt{-10 \, x^{2} - x + 3} x + \frac{327738785}{34420736} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) - \frac{441499355}{17210368} \, \sqrt{-10 \, x^{2} - x + 3} \]

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)^8,x, algorithm="maxima")

[Out]

122277415/271063296*(-10*x^2 - x + 3)^(5/2) + 3/49*(-10*x^2 - x + 3)^(7/2)/(2187
*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)
+ 37/196*(-10*x^2 - x + 3)^(7/2)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 216
0*x^2 + 576*x + 64) + 1369/2744*(-10*x^2 - x + 3)^(7/2)/(243*x^5 + 810*x^4 + 108
0*x^3 + 720*x^2 + 240*x + 32) + 162319/153664*(-10*x^2 - x + 3)^(7/2)/(81*x^4 +
216*x^3 + 216*x^2 + 96*x + 16) + 3024121/2151296*(-10*x^2 - x + 3)^(7/2)/(27*x^3
+ 54*x^2 + 36*x + 8) + 24455483/60236288*(-10*x^2 - x + 3)^(7/2)/(9*x^2 + 12*x
+ 4) - 2190708025/180708864*(-10*x^2 - x + 3)^(3/2)*x + 4205402795/361417728*(-1
0*x^2 - x + 3)^(3/2) - 4059472427/1084253184*(-10*x^2 - x + 3)^(5/2)/(3*x + 2) +
501088225/8605184*sqrt(-10*x^2 - x + 3)*x + 327738785/34420736*sqrt(7)*arcsin(3
7/11*x/abs(3*x + 2) + 20/11/abs(3*x + 2)) - 441499355/17210368*sqrt(-10*x^2 - x
+ 3)

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Fricas [A]  time = 0.231351, size = 208, normalized size = 0.87 \[ \frac{\sqrt{7}{\left (2 \, \sqrt{7}{\left (62659925205 \, x^{6} + 253441751890 \, x^{5} + 427105196104 \, x^{4} + 384048502848 \, x^{3} + 194338741616 \, x^{2} + 52456780256 \, x + 5897927808\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 983216355 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{103262208 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

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)^8,x, algorithm="fricas")

[Out]

1/103262208*sqrt(7)*(2*sqrt(7)*(62659925205*x^6 + 253441751890*x^5 + 42710519610
4*x^4 + 384048502848*x^3 + 194338741616*x^2 + 52456780256*x + 5897927808)*sqrt(5
*x + 3)*sqrt(-2*x + 1) + 983216355*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4
+ 15120*x^3 + 6048*x^2 + 1344*x + 128)*arctan(1/14*sqrt(7)*(37*x + 20)/(sqrt(5*
x + 3)*sqrt(-2*x + 1))))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x
^3 + 6048*x^2 + 1344*x + 128)

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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)**8,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.80285, size = 759, normalized size = 3.19 \[ \frac{65547757}{68841472} \, \sqrt{70} \sqrt{10}{\left (\pi + 2 \, \arctan \left (-\frac{\sqrt{70} \sqrt{5 \, x + 3}{\left (\frac{{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}\right )\right )} - \frac{8857805 \,{\left (111 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{13} + 207200 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{11} + 164185280 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{9} - 63583027200 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{7} - 12872125952000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{5} - 1273567232000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{3} - 53489823744000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}\right )}}{3687936 \,{\left ({\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{2} + 280\right )}^{7}} \]

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)^8,x, algorithm="giac")

[Out]

65547757/68841472*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)))) - 8857805/3687936*(111*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 +
207200*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 + 164185280*sqrt(10)*((sqrt(2)*sq
rt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x +
5) - sqrt(22)))^9 - 63583027200*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/s
qrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^7 - 1287212
5952000*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 - 1273567232000000*sqrt(10)*((sqr
t(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 - 53489823744000000*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)^7