3.2393 \(\int \frac{(1-2 x)^{5/2} (3+5 x)^{3/2}}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=238 \[ -\frac{(5 x+3)^{3/2} (1-2 x)^{5/2}}{21 (3 x+2)^7}+\frac{115 (5 x+3)^{3/2} (1-2 x)^{3/2}}{756 (3 x+2)^6}+\frac{1921 (5 x+3)^{3/2} \sqrt{1-2 x}}{1512 (3 x+2)^5}+\frac{40175505215 \sqrt{5 x+3} \sqrt{1-2 x}}{597445632 (3 x+2)}+\frac{384136145 \sqrt{5 x+3} \sqrt{1-2 x}}{42674688 (3 x+2)^2}+\frac{2199649 \sqrt{5 x+3} \sqrt{1-2 x}}{1524096 (3 x+2)^3}-\frac{443563 \sqrt{5 x+3} \sqrt{1-2 x}}{254016 (3 x+2)^4}-\frac{1891543995 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{2458624 \sqrt{7}} \]

[Out]

(-443563*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(254016*(2 + 3*x)^4) + (2199649*Sqrt[1 - 2
*x]*Sqrt[3 + 5*x])/(1524096*(2 + 3*x)^3) + (384136145*Sqrt[1 - 2*x]*Sqrt[3 + 5*x
])/(42674688*(2 + 3*x)^2) + (40175505215*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(597445632
*(2 + 3*x)) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^7) + (115*(1 - 2*x
)^(3/2)*(3 + 5*x)^(3/2))/(756*(2 + 3*x)^6) + (1921*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)
)/(1512*(2 + 3*x)^5) - (1891543995*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]
)/(2458624*Sqrt[7])

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Rubi [A]  time = 0.522877, 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 \[ -\frac{(5 x+3)^{3/2} (1-2 x)^{5/2}}{21 (3 x+2)^7}+\frac{115 (5 x+3)^{3/2} (1-2 x)^{3/2}}{756 (3 x+2)^6}+\frac{1921 (5 x+3)^{3/2} \sqrt{1-2 x}}{1512 (3 x+2)^5}+\frac{40175505215 \sqrt{5 x+3} \sqrt{1-2 x}}{597445632 (3 x+2)}+\frac{384136145 \sqrt{5 x+3} \sqrt{1-2 x}}{42674688 (3 x+2)^2}+\frac{2199649 \sqrt{5 x+3} \sqrt{1-2 x}}{1524096 (3 x+2)^3}-\frac{443563 \sqrt{5 x+3} \sqrt{1-2 x}}{254016 (3 x+2)^4}-\frac{1891543995 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{2458624 \sqrt{7}} \]

Antiderivative was successfully verified.

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

[Out]

(-443563*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(254016*(2 + 3*x)^4) + (2199649*Sqrt[1 - 2
*x]*Sqrt[3 + 5*x])/(1524096*(2 + 3*x)^3) + (384136145*Sqrt[1 - 2*x]*Sqrt[3 + 5*x
])/(42674688*(2 + 3*x)^2) + (40175505215*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(597445632
*(2 + 3*x)) - ((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(21*(2 + 3*x)^7) + (115*(1 - 2*x
)^(3/2)*(3 + 5*x)^(3/2))/(756*(2 + 3*x)^6) + (1921*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2)
)/(1512*(2 + 3*x)^5) - (1891543995*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]
)/(2458624*Sqrt[7])

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Rubi in Sympy [A]  time = 52.1583, size = 218, normalized size = 0.92 \[ - \frac{115 \left (- 2 x + 1\right )^{\frac{5}{2}} \sqrt{5 x + 3}}{5292 \left (3 x + 2\right )^{6}} - \frac{\left (- 2 x + 1\right )^{\frac{5}{2}} \left (5 x + 3\right )^{\frac{3}{2}}}{21 \left (3 x + 2\right )^{7}} + \frac{29 \left (- 2 x + 1\right )^{\frac{3}{2}} \sqrt{5 x + 3}}{504 \left (3 x + 2\right )^{5}} + \frac{40175505215 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{597445632 \left (3 x + 2\right )} + \frac{384136145 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{42674688 \left (3 x + 2\right )^{2}} + \frac{2199649 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{1524096 \left (3 x + 2\right )^{3}} + \frac{9083 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{36288 \left (3 x + 2\right )^{4}} - \frac{1891543995 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{17210368} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-115*(-2*x + 1)**(5/2)*sqrt(5*x + 3)/(5292*(3*x + 2)**6) - (-2*x + 1)**(5/2)*(5*
x + 3)**(3/2)/(21*(3*x + 2)**7) + 29*(-2*x + 1)**(3/2)*sqrt(5*x + 3)/(504*(3*x +
2)**5) + 40175505215*sqrt(-2*x + 1)*sqrt(5*x + 3)/(597445632*(3*x + 2)) + 38413
6145*sqrt(-2*x + 1)*sqrt(5*x + 3)/(42674688*(3*x + 2)**2) + 2199649*sqrt(-2*x +
1)*sqrt(5*x + 3)/(1524096*(3*x + 2)**3) + 9083*sqrt(-2*x + 1)*sqrt(5*x + 3)/(362
88*(3*x + 2)**4) - 1891543995*sqrt(7)*atan(sqrt(7)*sqrt(-2*x + 1)/(7*sqrt(5*x +
3)))/17210368

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Mathematica [A]  time = 0.14986, size = 97, normalized size = 0.41 \[ \frac{\frac{14 \sqrt{1-2 x} \sqrt{5 x+3} \left (120526515645 x^6+487483968610 x^5+821723878536 x^4+738910550592 x^3+373848853744 x^2+100906793184 x+11351210112\right )}{(3 x+2)^7}-1891543995 \sqrt{7} \tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{34420736} \]

Antiderivative was successfully verified.

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

[Out]

((14*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(11351210112 + 100906793184*x + 373848853744*x^
2 + 738910550592*x^3 + 821723878536*x^4 + 487483968610*x^5 + 120526515645*x^6))/
(2 + 3*x)^7 - 1891543995*Sqrt[7]*ArcTan[(-20 - 37*x)/(2*Sqrt[7 - 14*x]*Sqrt[3 +
5*x])])/34420736

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Maple [B]  time = 0.02, size = 394, normalized size = 1.7 \[{\frac{1}{34420736\, \left ( 2+3\,x \right ) ^{7}}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 4136806717065\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{7}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{6}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{5}[phone]\,{x}^{6}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{4}[phone]\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{3}[phone]\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{2}[phone]\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) x+5233883952416\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) [phone]\,x\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/34420736*(1-2*x)^(1/2)*(3+5*x)^(1/2)*(4136806717065*7^(1/2)*arctan(1/14*(37*x+
20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^7+19305098012970*7^(1/2)*arctan(1/14*(37*x+20
)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^6+38610196025940*7^(1/2)*arctan(1/14*(37*x+20)*
7^(1/2)/(-10*x^2-x+3)^(1/2))*x^5+1687371219030*x^6*(-10*x^2-x+3)^(1/2)[phone]
06600*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^4+68247755605
40*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+11504134299504*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+10344747708288*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+5233883952416*x^2*(-10*x^2-x+3)^(1/2)[phone]*7^(1/2)*arcta
n(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 = 1.53137, size = 437, normalized size = 1.84 \[ \frac{118356975}{4302592} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} + \frac{{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{7 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + \frac{305 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{588 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{2161 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{1176 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{129195 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{21952 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{4780215 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{307328 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{213042555 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{8605184 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{2892030075}{8605184} \, \sqrt{-10 \, x^{2} - x + 3} x + \frac{1891543995}{34420736} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) - \frac{2548112985}{17210368} \, \sqrt{-10 \, x^{2} - x + 3} + \frac{280970415 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{17210368 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

118356975/4302592*(-10*x^2 - x + 3)^(3/2) + 1/7*(-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) + 3
05/588*(-10*x^2 - x + 3)^(5/2)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*
x^2 + 576*x + 64) + 2161/1176*(-10*x^2 - x + 3)^(5/2)/(243*x^5 + 810*x^4 + 1080*
x^3 + 720*x^2 + 240*x + 32) + 129195/21952*(-10*x^2 - x + 3)^(5/2)/(81*x^4 + 216
*x^3 + 216*x^2 + 96*x + 16) + 4780215/307328*(-10*x^2 - x + 3)^(5/2)/(27*x^3 + 5
4*x^2 + 36*x + 8) + 213042555/8605184*(-10*x^2 - x + 3)^(5/2)/(9*x^2 + 12*x + 4)
+ 2892030075/8605184*sqrt(-10*x^2 - x + 3)*x + 1891543995/34420736*sqrt(7)*arcs
in(37/11*x/abs(3*x + 2) + 20/11/abs(3*x + 2)) - 2548112985/17210368*sqrt(-10*x^2
- x + 3) + 280970415/17210368*(-10*x^2 - x + 3)^(3/2)/(3*x + 2)

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Fricas [A]  time = 0.235074, size = 208, normalized size = 0.87 \[ \frac{\sqrt{7}{\left (2 \, \sqrt{7}{\left (120526515645 \, x^{6} + 487483968610 \, x^{5} + 821723878536 \, x^{4} + 738910550592 \, x^{3} + 373848853744 \, x^{2} + 100906793184 \, x + 11351210112\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 1891543995 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{34420736 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/34420736*sqrt(7)*(2*sqrt(7)*(120526515645*x^6 + 487483968610*x^5 + 82172387853
6*x^4 + 738910550592*x^3 + 373848853744*x^2 + 100906793184*x + 11351210112)*sqrt
(5*x + 3)*sqrt(-2*x + 1) + 1891543995*(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 + 1512
0*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)**(3/2)/(2+3*x)**8,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.755974, size = 759, normalized size = 3.19 \[ \frac{378308799}{68841472} \, \sqrt{70} \sqrt{10}{\left (\pi + 2 \, \arctan \left (-\frac{\sqrt{70} \sqrt{5 \, x + 3}{\left (\frac{{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}\right )\right )} - \frac{805255 \,{\left (2349 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{13} + 4384800 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{11} - 4393081280 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{9} - 1503513804800 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{7} - 272402016768000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{5} - 26951436288000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{3} - 1131960324096000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}\right )}}{1229312 \,{\left ({\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{2} + 280\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

378308799/68841472*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)))) - 805255/1229312*(2349*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 +
4384800*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 - 4393081280*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 - 1503513804800*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(2
2))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^7 - 27
2402016768000*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*s
qrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^5 - 26951436288000000*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 - 1131960324096000000*sqrt(10)*((sqrt(2)*sqrt(-1
0*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