3.2331 \(\int \frac{(1-2 x)^{3/2} (3+5 x)^{3/2}}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=238 \[ \frac{37 \sqrt{1-2 x} (5 x+3)^{3/2}}{252 (3 x+2)^6}-\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{21 (3 x+2)^7}+\frac{14677525921 \sqrt{1-2 x} \sqrt{5 x+3}}{464679936 (3 x+2)}+\frac{140331343 \sqrt{1-2 x} \sqrt{5 x+3}}{33191424 (3 x+2)^2}+\frac{4014523 \sqrt{1-2 x} \sqrt{5 x+3}}{5927040 (3 x+2)^3}+\frac{341917 \sqrt{1-2 x} \sqrt{5 x+3}}{2963520 (3 x+2)^4}-\frac{9901 \sqrt{1-2 x} \sqrt{5 x+3}}{52920 (3 x+2)^5}-\frac{6219452877 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{17210368 \sqrt{7}} \]

[Out]

(-9901*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(52920*(2 + 3*x)^5) + (341917*Sqrt[1 - 2*x]*
Sqrt[3 + 5*x])/(2963520*(2 + 3*x)^4) + (4014523*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(59
27040*(2 + 3*x)^3) + (140331343*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(33191424*(2 + 3*x)
^2) + (14677525921*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(464679936*(2 + 3*x)) - ((1 - 2*
x)^(3/2)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^7) + (37*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/
(252*(2 + 3*x)^6) - (6219452877*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(
17210368*Sqrt[7])

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Rubi [A]  time = 0.520051, antiderivative size = 238, normalized size of antiderivative = 1., number of steps used = 10, number of rules used = 6, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{37 \sqrt{1-2 x} (5 x+3)^{3/2}}{252 (3 x+2)^6}-\frac{(1-2 x)^{3/2} (5 x+3)^{3/2}}{21 (3 x+2)^7}+\frac{14677525921 \sqrt{1-2 x} \sqrt{5 x+3}}{464679936 (3 x+2)}+\frac{140331343 \sqrt{1-2 x} \sqrt{5 x+3}}{33191424 (3 x+2)^2}+\frac{4014523 \sqrt{1-2 x} \sqrt{5 x+3}}{5927040 (3 x+2)^3}+\frac{341917 \sqrt{1-2 x} \sqrt{5 x+3}}{2963520 (3 x+2)^4}-\frac{9901 \sqrt{1-2 x} \sqrt{5 x+3}}{52920 (3 x+2)^5}-\frac{6219452877 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{17210368 \sqrt{7}} \]

Antiderivative was successfully verified.

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

[Out]

(-9901*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(52920*(2 + 3*x)^5) + (341917*Sqrt[1 - 2*x]*
Sqrt[3 + 5*x])/(2963520*(2 + 3*x)^4) + (4014523*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(59
27040*(2 + 3*x)^3) + (140331343*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(33191424*(2 + 3*x)
^2) + (14677525921*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(464679936*(2 + 3*x)) - ((1 - 2*
x)^(3/2)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^7) + (37*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/
(252*(2 + 3*x)^6) - (6219452877*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(
17210368*Sqrt[7])

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Rubi in Sympy [A]  time = 52.6712, size = 218, normalized size = 0.92 \[ - \frac{37 \left (- 2 x + 1\right )^{\frac{3}{2}} \sqrt{5 x + 3}}{1764 \left (3 x + 2\right )^{6}} - \frac{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{\frac{3}{2}}}{21 \left (3 x + 2\right )^{7}} + \frac{14677525921 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{464679936 \left (3 x + 2\right )} + \frac{140331343 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{33191424 \left (3 x + 2\right )^{2}} + \frac{4014523 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{5927040 \left (3 x + 2\right )^{3}} + \frac{341917 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{2963520 \left (3 x + 2\right )^{4}} + \frac{2309 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{52920 \left (3 x + 2\right )^{5}} - \frac{6219452877 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{120472576} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-37*(-2*x + 1)**(3/2)*sqrt(5*x + 3)/(1764*(3*x + 2)**6) - (-2*x + 1)**(3/2)*(5*x
+ 3)**(3/2)/(21*(3*x + 2)**7) + 14677525921*sqrt(-2*x + 1)*sqrt(5*x + 3)/(46467
9936*(3*x + 2)) + 140331343*sqrt(-2*x + 1)*sqrt(5*x + 3)/(33191424*(3*x + 2)**2)
+ 4014523*sqrt(-2*x + 1)*sqrt(5*x + 3)/(5927040*(3*x + 2)**3) + 341917*sqrt(-2*
x + 1)*sqrt(5*x + 3)/(2963520*(3*x + 2)**4) + 2309*sqrt(-2*x + 1)*sqrt(5*x + 3)/
(52920*(3*x + 2)**5) - 6219452877*sqrt(7)*atan(sqrt(7)*sqrt(-2*x + 1)/(7*sqrt(5*
x + 3)))/120472576

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Mathematica [A]  time = 0.156905, size = 121, normalized size = 0.51 \[ \frac{\frac{42 \sqrt{1-2 x} \sqrt{5 x+3} \left (73387629605 (3 x+2)^6+9823194010 (3 x+2)^5+1573693016 (3 x+2)^4+268062928 (3 x+2)^3+256794496 (3 x+2)^2-568556800 (3 x+2)[phone]\right )}{(3 x+2)^7}-2518878415185 \sqrt{7} \tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{97582786560} \]

Antiderivative was successfully verified.

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

[Out]

((42*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(86051840 - 568556800*(2 + 3*x) + 256794496*(2
+ 3*x)^2 + 268062928*(2 + 3*x)^3 + 1573693016*(2 + 3*x)^4 + 9823194010*(2 + 3*x)
^5 + 73387629605*(2 + 3*x)^6))/(2 + 3*x)^7 - 2518878415185*Sqrt[7]*ArcTan[(-20 -
37*x)/(2*Sqrt[7 - 14*x]*Sqrt[3 + 5*x])])/97582786560

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Maple [B]  time = 0.018, size = 394, normalized size = 1.7 \[{\frac{1}{1204725760\, \left ( 2+3\,x \right ) ^{7}}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 68009717209995\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{7}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{6}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{5}[phone]\,{x}^{6}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{4}[phone]\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{3}[phone]\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{2}[phone]\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) x+86046428675424\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) [phone]\,x\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1204725760*(1-2*x)^(1/2)*(3+5*x)^(1/2)*(68009717209995*7^(1/2)*arctan(1/14*(37
*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^7+317378680313310*7^(1/2)*arctan(1/14*(37*
x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^6+634757360626620*7^(1/2)*arctan(1/14*(37*x
+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^5+27740523990690*x^6*(-10*x^2-x+3)^(1/2)+705
285956251800*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^4+1121
99818408020*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+189128663195472*x^4*(-10*x^2-x+3)^(1/2)+18807
6255000480*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^2+170069
285459584*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+86046428675424*x^2*(-10*x^2-x+3)^(1/2)[phone]
80*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
)^7

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Maxima [A]  time = 1.54285, size = 437, normalized size = 1.84 \[ \frac{1167483755}{90354432} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} + \frac{3 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{49 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + \frac{333 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{1372 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{11841 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{13720 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{424797 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{153664 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{15717489 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{2151296 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{700490253 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{60236288 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{9509080845}{60236288} \, \sqrt{-10 \, x^{2} - x + 3} x + \frac{6219452877}{240945152} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) - \frac{8378271231}{120472576} \, \sqrt{-10 \, x^{2} - x + 3} + \frac{2771517227 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{361417728 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^(3/2)*(-2*x + 1)^(3/2)/(3*x + 2)^8,x, algorithm="maxima")

[Out]

1167483755/90354432*(-10*x^2 - x + 3)^(3/2) + 3/49*(-10*x^2 - x + 3)^(5/2)/(2187
*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)
+ 333/1372*(-10*x^2 - x + 3)^(5/2)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2
160*x^2 + 576*x + 64) + 11841/13720*(-10*x^2 - x + 3)^(5/2)/(243*x^5 + 810*x^4 +
1080*x^3 + 720*x^2 + 240*x + 32) + 424797/153664*(-10*x^2 - x + 3)^(5/2)/(81*x^
4 + 216*x^3 + 216*x^2 + 96*x + 16) + 15717489/2151296*(-10*x^2 - x + 3)^(5/2)/(2
7*x^3 + 54*x^2 + 36*x + 8) + 700490253/60236288*(-10*x^2 - x + 3)^(5/2)/(9*x^2 +
12*x + 4) + 9509080845/60236288*sqrt(-10*x^2 - x + 3)*x + 6219452877/240945152*
sqrt(7)*arcsin(37/11*x/abs(3*x + 2) + 20/11/abs(3*x + 2)) - 8378271231/120472576
*sqrt(-10*x^2 - x + 3) + 2771517227/361417728*(-10*x^2 - x + 3)^(3/2)/(3*x + 2)

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Fricas [A]  time = 0.23272, size = 208, normalized size = 0.87 \[ \frac{\sqrt{7}{\left (2 \, \sqrt{7}{\left (1981465999335 \, x^{6} + 8014272743430 \, x^{5} + 13509190228248 \, x^{4} + 12147806104256 \, x^{3} + 6146173476816 \, x^{2} + 1658923773088 \, x + 186609267072\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 31097264385 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{1204725760 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^(3/2)*(-2*x + 1)^(3/2)/(3*x + 2)^8,x, algorithm="fricas")

[Out]

1/1204725760*sqrt(7)*(2*sqrt(7)*(1981465999335*x^6 + 8014272743430*x^5 + 1350919
0228248*x^4 + 12147806104256*x^3 + 6146173476816*x^2 + 1658923773088*x + 1866092
67072)*sqrt(5*x + 3)*sqrt(-2*x + 1) + 31097264385*(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 + 2268
0*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)**(3/2)*(3+5*x)**(3/2)/(2+3*x)**8,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.698365, size = 759, normalized size = 3.19 \[ \frac{6219452877}{2409451520} \, \sqrt{70} \sqrt{10}{\left (\pi + 2 \, \arctan \left (-\frac{\sqrt{70} \sqrt{5 \, x + 3}{\left (\frac{{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}\right )\right )} - \frac{14641 \,{\left (424797 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{13} + 792954400 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{11} - 748492373440 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{9} - 270037116518400 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{7} - 49241484970496000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{5} - 4873941796864000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{3} - 204705555468288000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}\right )}}{8605184 \,{\left ({\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{2} + 280\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^(3/2)*(-2*x + 1)^(3/2)/(3*x + 2)^8,x, algorithm="giac")

[Out]

6219452877/2409451520*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)))) - 14641/8605184*(424797*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 + 792954400*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 - 748492373440*sqrt(10)*(
(sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sq
rt(-10*x + 5) - sqrt(22)))^9 - 270037116518400*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 - 49241484970496000*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 - 4873941796864
000000*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 - 204705555468288000000*sqrt(10)*(
(sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sq
rt(-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