3.2343 \(\int \frac{(1-2 x)^{3/2} (3+5 x)^{5/2}}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=238 \[ \frac{181 \sqrt{1-2 x} (5 x+3)^{5/2}}{756 (3 x+2)^6}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2}}{21 (3 x+2)^7}-\frac{12421 \sqrt{1-2 x} (5 x+3)^{3/2}}{52920 (3 x+2)^5}+\frac{23466191827 \sqrt{1-2 x} \sqrt{5 x+3}}{4182119424 (3 x+2)}+\frac{224018941 \sqrt{1-2 x} \sqrt{5 x+3}}{298722816 (3 x+2)^2}+\frac{6249601 \sqrt{1-2 x} \sqrt{5 x+3}}{53343360 (3 x+2)^3}-\frac{1289227 \sqrt{1-2 x} \sqrt{5 x+3}}{8890560 (3 x+2)^4}-\frac{1104970911 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{17210368 \sqrt{7}} \]

[Out]

(-1289227*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(8890560*(2 + 3*x)^4) + (6249601*Sqrt[1 -
2*x]*Sqrt[3 + 5*x])/(53343360*(2 + 3*x)^3) + (224018941*Sqrt[1 - 2*x]*Sqrt[3 +
5*x])/(298722816*(2 + 3*x)^2) + (23466191827*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(41821
19424*(2 + 3*x)) - (12421*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(52920*(2 + 3*x)^5) - (
(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(21*(2 + 3*x)^7) + (181*Sqrt[1 - 2*x]*(3 + 5*x)
^(5/2))/(756*(2 + 3*x)^6) - (1104970911*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5
*x])])/(17210368*Sqrt[7])

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Rubi [A]  time = 0.534199, 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 \[ \frac{181 \sqrt{1-2 x} (5 x+3)^{5/2}}{756 (3 x+2)^6}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2}}{21 (3 x+2)^7}-\frac{12421 \sqrt{1-2 x} (5 x+3)^{3/2}}{52920 (3 x+2)^5}+\frac{23466191827 \sqrt{1-2 x} \sqrt{5 x+3}}{4182119424 (3 x+2)}+\frac{224018941 \sqrt{1-2 x} \sqrt{5 x+3}}{298722816 (3 x+2)^2}+\frac{6249601 \sqrt{1-2 x} \sqrt{5 x+3}}{53343360 (3 x+2)^3}-\frac{1289227 \sqrt{1-2 x} \sqrt{5 x+3}}{8890560 (3 x+2)^4}-\frac{1104970911 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{17210368 \sqrt{7}} \]

Antiderivative was successfully verified.

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

[Out]

(-1289227*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(8890560*(2 + 3*x)^4) + (6249601*Sqrt[1 -
2*x]*Sqrt[3 + 5*x])/(53343360*(2 + 3*x)^3) + (224018941*Sqrt[1 - 2*x]*Sqrt[3 +
5*x])/(298722816*(2 + 3*x)^2) + (23466191827*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(41821
19424*(2 + 3*x)) - (12421*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(52920*(2 + 3*x)^5) - (
(1 - 2*x)^(3/2)*(3 + 5*x)^(5/2))/(21*(2 + 3*x)^7) + (181*Sqrt[1 - 2*x]*(3 + 5*x)
^(5/2))/(756*(2 + 3*x)^6) - (1104970911*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5
*x])])/(17210368*Sqrt[7])

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Rubi in Sympy [A]  time = 52.0745, size = 218, normalized size = 0.92 \[ - \frac{7489 \left (- 2 x + 1\right )^{\frac{3}{2}} \sqrt{5 x + 3}}{370440 \left (3 x + 2\right )^{5}} - \frac{181 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{\frac{3}{2}}}{5292 \left (3 x + 2\right )^{6}} - \frac{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{\frac{5}{2}}}{21 \left (3 x + 2\right )^{7}} + \frac{23466191827 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{4182119424 \left (3 x + 2\right )} + \frac{224018941 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{298722816 \left (3 x + 2\right )^{2}} + \frac{6249601 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{53343360 \left (3 x + 2\right )^{3}} + \frac{98267 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{1270080 \left (3 x + 2\right )^{4}} - \frac{1104970911 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{120472576} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7489*(-2*x + 1)**(3/2)*sqrt(5*x + 3)/(370440*(3*x + 2)**5) - 181*(-2*x + 1)**(3
/2)*(5*x + 3)**(3/2)/(5292*(3*x + 2)**6) - (-2*x + 1)**(3/2)*(5*x + 3)**(5/2)/(2
1*(3*x + 2)**7) + 23466191827*sqrt(-2*x + 1)*sqrt(5*x + 3)/(4182119424*(3*x + 2)
) + 224018941*sqrt(-2*x + 1)*sqrt(5*x + 3)/(298722816*(3*x + 2)**2) + 6249601*sq
rt(-2*x + 1)*sqrt(5*x + 3)/(53343360*(3*x + 2)**3) + 98267*sqrt(-2*x + 1)*sqrt(5
*x + 3)/(1270080*(3*x + 2)**4) - 1104970911*sqrt(7)*atan(sqrt(7)*sqrt(-2*x + 1)/
(7*sqrt(5*x + 3)))/120472576

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Mathematica [A]  time = 0.150331, size = 97, normalized size = 0.41 \[ \frac{\frac{14 \sqrt{1-2 x} \sqrt{5 x+3} \left (351992877405 x^6+1423652835490 x^5+2399706883464 x^4+2158260396608 x^3+1092179419888 x^2+294736348384 x+33120084096\right )}{(3 x+2)^7}-5524854555 \sqrt{7} \tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{1204725760} \]

Antiderivative was successfully verified.

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

[Out]

((14*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(33120084096 + 294736348384*x + 1092179419888*x
^2 + 2158260396608*x^3 + 2399706883464*x^4 + 1423652835490*x^5 + 351992877405*x^
6))/(2 + 3*x)^7 - 5524854555*Sqrt[7]*ArcTan[(-20 - 37*x)/(2*Sqrt[7 - 14*x]*Sqrt[
3 + 5*x])])/1204725760

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Maple [B]  time = 0.021, size = 394, normalized size = 1.7 \[{\frac{1}{1204725760\, \left ( 2+3\,x \right ) ^{7}}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 12082856911785\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{7}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{6}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{5}[phone]\,{x}^{6}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{4}[phone]\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{3}[phone]\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{2}[phone]\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) x+15290511878432\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) [phone]\,x\sqrt{-10\,{x}^{2}-x+3}[phone]\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1204725760*(1-2*x)^(1/2)*(3+5*x)^(1/2)*(12082856911785*7^(1/2)*arctan(1/14*(37
*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^7+56386665588330*7^(1/2)*arctan(1/14*(37*x
+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^6+112773331176660*7^(1/2)*arctan(1/14*(37*x+
20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^5+4927900283670*x^6*(-10*x^2-x+3)^(1/2)+12530
3701307400*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^4+199311
39696860*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+33595896368496*x^4*(-10*x^2-x+3)^(1/2)[phone]
8640*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^2+302156455525
12*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+15290511878432*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)^7

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Maxima [A]  time = 1.52321, size = 437, normalized size = 1.84 \[ \frac{207419465}{90354432} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} - \frac{{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{49 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + \frac{157 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{4116 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{6289 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{41160 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{75471 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{153664 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{2792427 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{2151296 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{124451679 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{5}{2}}}{60236288 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{1689418335}{60236288} \, \sqrt{-10 \, x^{2} - x + 3} x + \frac{1104970911}{240945152} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) - \frac{1488514533}{120472576} \, \sqrt{-10 \, x^{2} - x + 3} + \frac{492397961 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{361417728 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

207419465/90354432*(-10*x^2 - x + 3)^(3/2) - 1/49*(-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) +
157/4116*(-10*x^2 - x + 3)^(5/2)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 21
60*x^2 + 576*x + 64) + 6289/41160*(-10*x^2 - x + 3)^(5/2)/(243*x^5 + 810*x^4 + 1
080*x^3 + 720*x^2 + 240*x + 32) + 75471/153664*(-10*x^2 - x + 3)^(5/2)/(81*x^4 +
216*x^3 + 216*x^2 + 96*x + 16) + 2792427/2151296*(-10*x^2 - x + 3)^(5/2)/(27*x^
3 + 54*x^2 + 36*x + 8) + 124451679/60236288*(-10*x^2 - x + 3)^(5/2)/(9*x^2 + 12*
x + 4) + 1689418335/60236288*sqrt(-10*x^2 - x + 3)*x + 1104970911/240945152*sqrt
(7)*arcsin(37/11*x/abs(3*x + 2) + 20/11/abs(3*x + 2)) - 1488514533/120472576*sqr
t(-10*x^2 - x + 3) + 492397961/361417728*(-10*x^2 - x + 3)^(3/2)/(3*x + 2)

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Fricas [A]  time = 0.237634, size = 208, normalized size = 0.87 \[ \frac{\sqrt{7}{\left (2 \, \sqrt{7}{\left (351992877405 \, x^{6} + 1423652835490 \, x^{5} + 2399706883464 \, x^{4} + 2158260396608 \, x^{3} + 1092179419888 \, x^{2} + 294736348384 \, x + 33120084096\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 5524854555 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{1204725760 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1204725760*sqrt(7)*(2*sqrt(7)*(351992877405*x^6 + 1423652835490*x^5 + 23997068
83464*x^4 + 2158260396608*x^3 + 1092179419888*x^2 + 294736348384*x + 33120084096
)*sqrt(5*x + 3)*sqrt(-2*x + 1) + 5524854555*(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)**(3/2)*(3+5*x)**(5/2)/(2+3*x)**8,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.730009, size = 759, normalized size = 3.19 \[ \frac{1104970911}{2409451520} \, \sqrt{70} \sqrt{10}{\left (\pi + 2 \, \arctan \left (-\frac{\sqrt{70} \sqrt{5 \, x + 3}{\left (\frac{{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}\right )\right )} - \frac{161051 \,{\left (6861 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{13} + 12807200 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{11} + 10148425280 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{9} - 3461100339200 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{7} - 785566018048000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{5} - 78720223232000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{3} - 3306249375744000000 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}\right )}}{8605184 \,{\left ({\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{2} + 280\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1104970911/2409451520*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)))) - 161051/8605184*(6861*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - s
qrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^1
3 + 12807200*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sq
rt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^11 + 10148425280*sqrt(10)*((sq
rt(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 - 3461100339200*sqrt(10)*((sqrt(2)*sqrt(-10*x + 5) - s
qrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^7
- 785566018048000*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 - 78720223232000000*sq
rt(10)*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sq
rt(2)*sqrt(-10*x + 5) - sqrt(22)))^3 - 3306249375744000000*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))))/(((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