3.2281 \(\int \frac{\sqrt{1-2 x} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=238 \[ -\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{21 (3 x+2)^7}-\frac{59 \sqrt{1-2 x} (5 x+3)^{3/2}}{1764 (3 x+2)^6}+\frac{8818415317 \sqrt{1-2 x} \sqrt{5 x+3}}{3252759552 (3 x+2)}+\frac{84539611 \sqrt{1-2 x} \sqrt{5 x+3}}{232339968 (3 x+2)^2}+\frac{2524471 \sqrt{1-2 x} \sqrt{5 x+3}}{41489280 (3 x+2)^3}+\frac{369409 \sqrt{1-2 x} \sqrt{5 x+3}}{20744640 (3 x+2)^4}-\frac{6577 \sqrt{1-2 x} \sqrt{5 x+3}}{370440 (3 x+2)^5}-\frac{3735929329 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{120472576 \sqrt{7}} \]

[Out]

(-6577*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(370440*(2 + 3*x)^5) + (369409*Sqrt[1 - 2*x]
*Sqrt[3 + 5*x])/(20744640*(2 + 3*x)^4) + (2524471*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(
41489280*(2 + 3*x)^3) + (84539611*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(232339968*(2 + 3
*x)^2) + (8818415317*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(3252759552*(2 + 3*x)) - (59*S
qrt[1 - 2*x]*(3 + 5*x)^(3/2))/(1764*(2 + 3*x)^6) - (Sqrt[1 - 2*x]*(3 + 5*x)^(5/2
))/(21*(2 + 3*x)^7) - (3735929329*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])
/(120472576*Sqrt[7])

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Rubi [A]  time = 0.530673, 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 \[ -\frac{\sqrt{1-2 x} (5 x+3)^{5/2}}{21 (3 x+2)^7}-\frac{59 \sqrt{1-2 x} (5 x+3)^{3/2}}{1764 (3 x+2)^6}+\frac{8818415317 \sqrt{1-2 x} \sqrt{5 x+3}}{3252759552 (3 x+2)}+\frac{84539611 \sqrt{1-2 x} \sqrt{5 x+3}}{232339968 (3 x+2)^2}+\frac{2524471 \sqrt{1-2 x} \sqrt{5 x+3}}{41489280 (3 x+2)^3}+\frac{369409 \sqrt{1-2 x} \sqrt{5 x+3}}{20744640 (3 x+2)^4}-\frac{6577 \sqrt{1-2 x} \sqrt{5 x+3}}{370440 (3 x+2)^5}-\frac{3735929329 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{120472576 \sqrt{7}} \]

Antiderivative was successfully verified.

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

[Out]

(-6577*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(370440*(2 + 3*x)^5) + (369409*Sqrt[1 - 2*x]
*Sqrt[3 + 5*x])/(20744640*(2 + 3*x)^4) + (2524471*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(
41489280*(2 + 3*x)^3) + (84539611*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(232339968*(2 + 3
*x)^2) + (8818415317*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(3252759552*(2 + 3*x)) - (59*S
qrt[1 - 2*x]*(3 + 5*x)^(3/2))/(1764*(2 + 3*x)^6) - (Sqrt[1 - 2*x]*(3 + 5*x)^(5/2
))/(21*(2 + 3*x)^7) - (3735929329*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])
/(120472576*Sqrt[7])

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Rubi in Sympy [A]  time = 52.7782, size = 218, normalized size = 0.92 \[ \frac{8818415317 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{3252759552 \left (3 x + 2\right )} + \frac{84539611 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{232339968 \left (3 x + 2\right )^{2}} + \frac{2524471 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{41489280 \left (3 x + 2\right )^{3}} + \frac{369409 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{20744640 \left (3 x + 2\right )^{4}} - \frac{6577 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{370440 \left (3 x + 2\right )^{5}} - \frac{59 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}}{1764 \left (3 x + 2\right )^{6}} - \frac{\sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{5}{2}}}{21 \left (3 x + 2\right )^{7}} - \frac{3735929329 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{843308032} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

8818415317*sqrt(-2*x + 1)*sqrt(5*x + 3)/(3252759552*(3*x + 2)) + 84539611*sqrt(-
2*x + 1)*sqrt(5*x + 3)/(232339968*(3*x + 2)**2) + 2524471*sqrt(-2*x + 1)*sqrt(5*
x + 3)/(41489280*(3*x + 2)**3) + 369409*sqrt(-2*x + 1)*sqrt(5*x + 3)/(20744640*(
3*x + 2)**4) - 6577*sqrt(-2*x + 1)*sqrt(5*x + 3)/(370440*(3*x + 2)**5) - 59*sqrt
(-2*x + 1)*(5*x + 3)**(3/2)/(1764*(3*x + 2)**6) - sqrt(-2*x + 1)*(5*x + 3)**(5/2
)/(21*(3*x + 2)**7) - 3735929329*sqrt(7)*atan(sqrt(7)*sqrt(-2*x + 1)/(7*sqrt(5*x
+ 3)))/843308032

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Mathematica [A]  time = 0.144603, size = 97, normalized size = 0.41 \[ \frac{\frac{378 \sqrt{1-2 x} \sqrt{5 x+3} \left (3571458203385 x^6+14445612678330 x^5+24351227238888 x^4+21898948566336 x^3+11077661454896 x^2+2987299350368 x+335335888512\right )}{(3 x+2)^7}-1513051378245 \sqrt{7} \tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{683079505920} \]

Antiderivative was successfully verified.

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

[Out]

((378*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(335335888512 + 2987299350368*x + 110776614548
96*x^2 + 21898948566336*x^3 + 24351227238888*x^4 + 14445612678330*x^5 + 35714582
03385*x^6))/(2 + 3*x)^7 - 1513051378245*Sqrt[7]*ArcTan[(-20 - 37*x)/(2*Sqrt[7 -
14*x]*Sqrt[3 + 5*x])])/683079505920

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Maple [B]  time = 0.033, size = 394, normalized size = 1.7 \[{\frac{1}{25299240960\, \left ( 2+3\,x \right ) ^{7}}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 122557161637845\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{7}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{6}+1143866841953220\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{5}[phone]\,{x}^{6}\sqrt{-10\,{x}^{2}-x+3}+1270963157725800\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{4}[phone]\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{3}[phone]\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{2}[phone]\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) x+155087260368544\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) [phone]\,x\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/25299240960*(1-2*x)^(1/2)*(3+5*x)^(1/2)*(122557161637845*7^(1/2)*arctan(1/14*(
37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^7+571933420976610*7^(1/2)*arctan(1/14*(3
7*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^6+1143866841953220*7^(1/2)*arctan(1/14*(3
7*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^5+50000414847390*x^6*(-10*x^2-x+3)^(1/2)+
1270963157725800*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^4+
202238577496620*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+340917181344432*x^4*(-10*x^2-x+3)^(1/2)+3
38923508726880*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^2+30
6585279928704*x^3*(-10*x^2-x+3)^(1/2)[phone]*7^(1/2)*arctan(1/14*(37*x+2
0)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x+155087260368544*x^2*(-10*x^2-x+3)^(1/2)+717298
4311680*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))[phone]
2*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 = 1.5307, size = 398, normalized size = 1.67 \[ \frac{3735929329}{1686616064} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) + \frac{154377245}{90354432} \, \sqrt{-10 \, x^{2} - x + 3} + \frac{{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{147 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} - \frac{191 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{4116 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{919 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{96040 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{72203 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{768320 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{2612695 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{6453888 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{92626347 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{60236288 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{1142391613 \, \sqrt{-10 \, x^{2} - x + 3}}{361417728 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3735929329/1686616064*sqrt(7)*arcsin(37/11*x/abs(3*x + 2) + 20/11/abs(3*x + 2))
+ 154377245/90354432*sqrt(-10*x^2 - x + 3) + 1/147*(-10*x^2 - x + 3)^(3/2)/(2187
*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)
- 191/4116*(-10*x^2 - x + 3)^(3/2)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2
160*x^2 + 576*x + 64) + 919/96040*(-10*x^2 - x + 3)^(3/2)/(243*x^5 + 810*x^4 + 1
080*x^3 + 720*x^2 + 240*x + 32) + 72203/768320*(-10*x^2 - x + 3)^(3/2)/(81*x^4 +
216*x^3 + 216*x^2 + 96*x + 16) + 2612695/6453888*(-10*x^2 - x + 3)^(3/2)/(27*x^
3 + 54*x^2 + 36*x + 8) + 92626347/60236288*(-10*x^2 - x + 3)^(3/2)/(9*x^2 + 12*x
+ 4) - 1142391613/361417728*sqrt(-10*x^2 - x + 3)/(3*x + 2)

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Fricas [A]  time = 0.229504, size = 208, normalized size = 0.87 \[ \frac{\sqrt{7}{\left (2 \, \sqrt{7}{\left (3571458203385 \, x^{6} + 14445612678330 \, x^{5} + 24351227238888 \, x^{4} + 21898948566336 \, x^{3} + 11077661454896 \, x^{2} + 2987299350368 \, x + 335335888512\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 56038939935 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{25299240960 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/25299240960*sqrt(7)*(2*sqrt(7)*(3571458203385*x^6 + 14445612678330*x^5 + 24351
227238888*x^4 + 21898948566336*x^3 + 11077661454896*x^2 + 2987299350368*x + 3353
35888512)*sqrt(5*x + 3)*sqrt(-2*x + 1) + 56038939935*(2187*x^7 + 10206*x^6 + 204
12*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*arctan(1/14*sqrt(7)*(3
7*x + 20)/(sqrt(5*x + 3)*sqrt(-2*x + 1))))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 2
2680*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((3+5*x)**(5/2)*(1-2*x)**(1/2)/(2+3*x)**8,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.717447, size = 759, normalized size = 3.19 \[ \frac{3735929329}{16866160640} \, \sqrt{70} \sqrt{10}{\left (\pi + 2 \, \arctan \left (-\frac{\sqrt{70} \sqrt{5 \, x + 3}{\left (\frac{{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}\right )\right )} - \frac{14641 \,{\left (765507 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{13} + 1428946400 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{11} + 1132297127360 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{9} - 334448649830400 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{7} - 85378328229376000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{5} - 8754907317452800000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{3} - 368890400944128000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}\right )}}{180708864 \,{\left ({\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{2} + 280\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3735929329/16866160640*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)))) - 14641/180708864*(765507*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 + 1428946400*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 + 1132297127360*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 - 334448649830400*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) - sq
rt(22)))^7 - 85378328229376000*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sq
rt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^5 - 87549073
17452800000*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqr
t(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^3 - 368890400944128000000*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