3.2397 \(\int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^6} \, dx\)

Optimal. Leaf size=180 \[ \frac{3 (5 x+3)^{3/2} (1-2 x)^{7/2}}{35 (3 x+2)^5}+\frac{251 (5 x+3)^{3/2} (1-2 x)^{5/2}}{280 (3 x+2)^4}+\frac{2761 (5 x+3)^{3/2} (1-2 x)^{3/2}}{336 (3 x+2)^3}+\frac{30371 (5 x+3)^{3/2} \sqrt{1-2 x}}{448 (3 x+2)^2}-\frac{334081 \sqrt{5 x+3} \sqrt{1-2 x}}{6272 (3 x+2)}-\frac{3674891 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{6272 \sqrt{7}} \]

[Out]

(-334081*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(6272*(2 + 3*x)) + (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/(35*(2 + 3*x)^5)
+ (251*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(280*(2 + 3*x)^4) + (2761*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(336*(2 + 3
*x)^3) + (30371*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(448*(2 + 3*x)^2) - (3674891*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt
[3 + 5*x])])/(6272*Sqrt[7])

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Rubi [A]  time = 0.0525002, antiderivative size = 180, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 4, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {96, 94, 93, 204} \[ \frac{3 (5 x+3)^{3/2} (1-2 x)^{7/2}}{35 (3 x+2)^5}+\frac{251 (5 x+3)^{3/2} (1-2 x)^{5/2}}{280 (3 x+2)^4}+\frac{2761 (5 x+3)^{3/2} (1-2 x)^{3/2}}{336 (3 x+2)^3}+\frac{30371 (5 x+3)^{3/2} \sqrt{1-2 x}}{448 (3 x+2)^2}-\frac{334081 \sqrt{5 x+3} \sqrt{1-2 x}}{6272 (3 x+2)}-\frac{3674891 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{6272 \sqrt{7}} \]

Antiderivative was successfully verified.

[In]

Int[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^6,x]

[Out]

(-334081*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(6272*(2 + 3*x)) + (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/(35*(2 + 3*x)^5)
+ (251*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/(280*(2 + 3*x)^4) + (2761*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/(336*(2 + 3
*x)^3) + (30371*Sqrt[1 - 2*x]*(3 + 5*x)^(3/2))/(448*(2 + 3*x)^2) - (3674891*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt
[3 + 5*x])])/(6272*Sqrt[7])

Rule 96

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(b*(a +
b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*f)), x] + Dist[(a*d*f*(m + 1)
+ b*c*f*(n + 1) + b*d*e*(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*
x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, m, n, p}, x] && EqQ[Simplify[m + n + p + 3], 0] && (LtQ[m, -1] || Sum
SimplerQ[m, 1])

Rule 94

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[((a + b
*x)^(m + 1)*(c + d*x)^n*(e + f*x)^(p + 1))/((m + 1)*(b*e - a*f)), x] - Dist[(n*(d*e - c*f))/((m + 1)*(b*e - a*
f)), Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, m, p}, x] && EqQ[
m + n + p + 2, 0] && GtQ[n, 0] &&  !(SumSimplerQ[p, 1] &&  !SumSimplerQ[m, 1])

Rule 93

Int[(((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_))/((e_.) + (f_.)*(x_)), x_Symbol] :> With[{q = Denomin
ator[m]}, Dist[q, Subst[Int[x^(q*(m + 1) - 1)/(b*e - a*f - (d*e - c*f)*x^q), x], x, (a + b*x)^(1/q)/(c + d*x)^
(1/q)], x]] /; FreeQ[{a, b, c, d, e, f}, x] && EqQ[m + n + 1, 0] && RationalQ[n] && LtQ[-1, m, 0] && SimplerQ[
a + b*x, c + d*x]

Rule 204

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /
; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])

Rubi steps

\begin{align*} \int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^6} \, dx &=\frac{3 (1-2 x)^{7/2} (3+5 x)^{3/2}}{35 (2+3 x)^5}+\frac{251}{70} \int \frac{(1-2 x)^{5/2} \sqrt{3+5 x}}{(2+3 x)^5} \, dx\\ &=\frac{3 (1-2 x)^{7/2} (3+5 x)^{3/2}}{35 (2+3 x)^5}+\frac{251 (1-2 x)^{5/2} (3+5 x)^{3/2}}{280 (2+3 x)^4}+\frac{2761}{112} \int \frac{(1-2 x)^{3/2} \sqrt{3+5 x}}{(2+3 x)^4} \, dx\\ &=\frac{3 (1-2 x)^{7/2} (3+5 x)^{3/2}}{35 (2+3 x)^5}+\frac{251 (1-2 x)^{5/2} (3+5 x)^{3/2}}{280 (2+3 x)^4}+\frac{2761 (1-2 x)^{3/2} (3+5 x)^{3/2}}{336 (2+3 x)^3}+\frac{30371}{224} \int \frac{\sqrt{1-2 x} \sqrt{3+5 x}}{(2+3 x)^3} \, dx\\ &=\frac{3 (1-2 x)^{7/2} (3+5 x)^{3/2}}{35 (2+3 x)^5}+\frac{251 (1-2 x)^{5/2} (3+5 x)^{3/2}}{280 (2+3 x)^4}+\frac{2761 (1-2 x)^{3/2} (3+5 x)^{3/2}}{336 (2+3 x)^3}+\frac{30371 \sqrt{1-2 x} (3+5 x)^{3/2}}{448 (2+3 x)^2}+\frac{334081}{896} \int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} (2+3 x)^2} \, dx\\ &=-\frac{334081 \sqrt{1-2 x} \sqrt{3+5 x}}{6272 (2+3 x)}+\frac{3 (1-2 x)^{7/2} (3+5 x)^{3/2}}{35 (2+3 x)^5}+\frac{251 (1-2 x)^{5/2} (3+5 x)^{3/2}}{280 (2+3 x)^4}+\frac{2761 (1-2 x)^{3/2} (3+5 x)^{3/2}}{336 (2+3 x)^3}+\frac{30371 \sqrt{1-2 x} (3+5 x)^{3/2}}{448 (2+3 x)^2}+\frac{3674891 \int \frac{1}{\sqrt{1-2 x} (2+3 x) \sqrt{3+5 x}} \, dx}{12544}\\ &=-\frac{334081 \sqrt{1-2 x} \sqrt{3+5 x}}{6272 (2+3 x)}+\frac{3 (1-2 x)^{7/2} (3+5 x)^{3/2}}{35 (2+3 x)^5}+\frac{251 (1-2 x)^{5/2} (3+5 x)^{3/2}}{280 (2+3 x)^4}+\frac{2761 (1-2 x)^{3/2} (3+5 x)^{3/2}}{336 (2+3 x)^3}+\frac{30371 \sqrt{1-2 x} (3+5 x)^{3/2}}{448 (2+3 x)^2}+\frac{3674891 \operatorname{Subst}\left (\int \frac{1}{-7-x^2} \, dx,x,\frac{\sqrt{1-2 x}}{\sqrt{3+5 x}}\right )}{6272}\\ &=-\frac{334081 \sqrt{1-2 x} \sqrt{3+5 x}}{6272 (2+3 x)}+\frac{3 (1-2 x)^{7/2} (3+5 x)^{3/2}}{35 (2+3 x)^5}+\frac{251 (1-2 x)^{5/2} (3+5 x)^{3/2}}{280 (2+3 x)^4}+\frac{2761 (1-2 x)^{3/2} (3+5 x)^{3/2}}{336 (2+3 x)^3}+\frac{30371 \sqrt{1-2 x} (3+5 x)^{3/2}}{448 (2+3 x)^2}-\frac{3674891 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{3+5 x}}\right )}{6272 \sqrt{7}}\\ \end{align*}

Mathematica [A]  time = 0.193881, size = 164, normalized size = 0.91 \[ \frac{1}{70} \left (\frac{6 (5 x+3)^{3/2} (1-2 x)^{7/2}}{(3 x+2)^5}+\frac{251 \left (2352 (5 x+3)^{3/2} (1-2 x)^{5/2}+55 (3 x+2) \left (392 (1-2 x)^{3/2} (5 x+3)^{3/2}+33 (3 x+2) \left (7 \sqrt{1-2 x} \sqrt{5 x+3} (37 x+20)-121 \sqrt{7} (3 x+2)^2 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )\right )\right )\right )}{9408 (3 x+2)^4}\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[((1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/(2 + 3*x)^6,x]

[Out]

((6*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/(2 + 3*x)^5 + (251*(2352*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2) + 55*(2 + 3*x)*(
392*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2) + 33*(2 + 3*x)*(7*Sqrt[1 - 2*x]*Sqrt[3 + 5*x]*(20 + 37*x) - 121*Sqrt[7]*(2
+ 3*x)^2*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])]))))/(9408*(2 + 3*x)^4))/70

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Maple [B]  time = 0.01, size = 298, normalized size = 1.7 \begin{align*}{\frac{1}{1317120\, \left ( 2+3\,x \right ) ^{5}}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 13394977695\,\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) \sqrt{7}{x}^{5}[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]\,\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+15069932248\,{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}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^6,x)

[Out]

1/1317120*(1-2*x)^(1/2)*(3+5*x)^(1/2)*(13394977695*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*7^(1/2)*
x^5+44649925650*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^4+59533234200*7^(1/2)*arctan(1/14
*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x^3+5463777690*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+14813908620*x^3*(-10*x^2-x+3)^(1/2)[phone]*7^(1/2)*arctan(1/1
4*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))*x+15069932248*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)^5

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Maxima [A]  time = 3.03396, size = 267, normalized size = 1.48 \begin{align*} \frac{3674891}{87808} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) + \frac{151855}{4704} \, \sqrt{-10 \, x^{2} - x + 3} + \frac{7 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{15 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{73 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{40 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{2573 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{336 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{91113 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{3136 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{1123727 \, \sqrt{-10 \, x^{2} - x + 3}}{18816 \,{\left (3 \, x + 2\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^6,x, algorithm="maxima")

[Out]

3674891/87808*sqrt(7)*arcsin(37/11*x/abs(3*x + 2) + 20/11/abs(3*x + 2)) + 151855/4704*sqrt(-10*x^2 - x + 3) +
7/15*(-10*x^2 - x + 3)^(3/2)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32) + 73/40*(-10*x^2 - x + 3)^(
3/2)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16) + 2573/336*(-10*x^2 - x + 3)^(3/2)/(27*x^3 + 54*x^2 + 36*x + 8)
+ 91113/3136*(-10*x^2 - x + 3)^(3/2)/(9*x^2 + 12*x + 4) - 1123727/18816*sqrt(-10*x^2 - x + 3)/(3*x + 2)

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Fricas [A]  time = 1.5603, size = 441, normalized size = 2.45 \begin{align*} -\frac{55123365 \, \sqrt{7}{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \,{\left (10 \, x^{2} + x - 3\right )}}\right ) - 14 \,{\left (390269835 \, x^{4} + 1058136330 \, x^{3} + 1076423732 \, x^{2} + 487066088 \, x + 82697568\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1317120 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^6,x, algorithm="fricas")

[Out]

-1/1317120*(55123365*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x +
20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(390269835*x^4 + 1058136330*x^3 + 1076423732*x^2 + 48
7066088*x + 82697568)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**(5/2)*(3+5*x)**(1/2)/(2+3*x)**6,x)

[Out]

Timed out

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Giac [B]  time = 4.16765, size = 594, normalized size = 3.3 \begin{align*} \frac{3674891}{878080} \, \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 (753 \, \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} - 1524880 \, \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} - 503767040 \, \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} - 77139328000 \, \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} - 4628359680000 \, \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 )}}{9408 \,{\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 )}^{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^6,x, algorithm="giac")

[Out]

3674891/878080*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)))) - 14641/9408*(753*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 - 1524880*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 -
503767040*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 - 77139328000*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 - 4628359680000*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)^5