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

Optimal. Leaf size=160 \[ -\frac {1}{12} (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac {11}{48} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac {121}{256} \sqrt {5 x+3} (1-2 x)^{7/2}+\frac {1331 \sqrt {5 x+3} (1-2 x)^{5/2}}{7680}+\frac {14641 \sqrt {5 x+3} (1-2 x)^{3/2}}{30720}+\frac {161051 \sqrt {5 x+3} \sqrt {1-2 x}}{102400}+\frac {1771561 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )}{102400 \sqrt {10}} \]

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Rubi [A]  time = 0.05, antiderivative size = 160, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {50, 54, 216} \begin {gather*} -\frac {1}{12} (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac {11}{48} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac {121}{256} \sqrt {5 x+3} (1-2 x)^{7/2}+\frac {1331 \sqrt {5 x+3} (1-2 x)^{5/2}}{7680}+\frac {14641 \sqrt {5 x+3} (1-2 x)^{3/2}}{30720}+\frac {161051 \sqrt {5 x+3} \sqrt {1-2 x}}{102400}+\frac {1771561 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )}{102400 \sqrt {10}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(161051*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/102400 + (14641*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/30720 + (1331*(1 - 2*x)^(5
/2)*Sqrt[3 + 5*x])/7680 - (121*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x])/256 - (11*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/48 -
((1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/12 + (1771561*ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]])/(102400*Sqrt[10])

Rule 50

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^n)/(b*
(m + n + 1)), x] + Dist[(n*(b*c - a*d))/(b*(m + n + 1)), Int[(a + b*x)^m*(c + d*x)^(n - 1), x], x] /; FreeQ[{a
, b, c, d}, x] && NeQ[b*c - a*d, 0] && GtQ[n, 0] && NeQ[m + n + 1, 0] &&  !(IGtQ[m, 0] && ( !IntegerQ[n] || (G
tQ[m, 0] && LtQ[m - n, 0]))) &&  !ILtQ[m + n + 2, 0] && IntLinearQ[a, b, c, d, m, n, x]

Rule 54

Int[1/(Sqrt[(a_.) + (b_.)*(x_)]*Sqrt[(c_.) + (d_.)*(x_)]), x_Symbol] :> Dist[2/Sqrt[b], Subst[Int[1/Sqrt[b*c -
a*d + d*x^2], x], x, Sqrt[a + b*x]], x] /; FreeQ[{a, b, c, d}, x] && GtQ[b*c - a*d, 0] && GtQ[b, 0]

Rule 216

Int[1/Sqrt[(a_) + (b_.)*(x_)^2], x_Symbol] :> Simp[ArcSin[(Rt[-b, 2]*x)/Sqrt[a]]/Rt[-b, 2], x] /; FreeQ[{a, b}
, x] && GtQ[a, 0] && NegQ[b]

Rubi steps

\begin {align*} \int (1-2 x)^{5/2} (3+5 x)^{5/2} \, dx &=-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {55}{24} \int (1-2 x)^{5/2} (3+5 x)^{3/2} \, dx\\ &=-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {121}{32} \int (1-2 x)^{5/2} \sqrt {3+5 x} \, dx\\ &=-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1331}{512} \int \frac {(1-2 x)^{5/2}}{\sqrt {3+5 x}} \, dx\\ &=\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {14641 \int \frac {(1-2 x)^{3/2}}{\sqrt {3+5 x}} \, dx}{3072}\\ &=\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {161051 \int \frac {\sqrt {1-2 x}}{\sqrt {3+5 x}} \, dx}{20480}\\ &=\frac {161051 \sqrt {1-2 x} \sqrt {3+5 x}}{102400}+\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1771561 \int \frac {1}{\sqrt {1-2 x} \sqrt {3+5 x}} \, dx}{204800}\\ &=\frac {161051 \sqrt {1-2 x} \sqrt {3+5 x}}{102400}+\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1771561 \operatorname {Subst}\left (\int \frac {1}{\sqrt {11-2 x^2}} \, dx,x,\sqrt {3+5 x}\right )}{102400 \sqrt {5}}\\ &=\frac {161051 \sqrt {1-2 x} \sqrt {3+5 x}}{102400}+\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1771561 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )}{102400 \sqrt {10}}\\ \end {align*}

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Mathematica [A]  time = 0.09, size = 84, normalized size = 0.52 \begin {gather*} \frac {5314683 \sqrt {20 x-10} \sinh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {2 x-1}\right )-10 \sqrt {5 x+3} \left (10240000 x^6-2560000 x^5-11091200 x^4+3408320 x^3+4538680 x^2-1703014 x-96003\right )}{3072000 \sqrt {1-2 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-10*Sqrt[3 + 5*x]*(-96003 - 1703014*x + 4538680*x^2 + 3408320*x^3 - 11091200*x^4 - 2560000*x^5 + 10240000*x^6
) + 5314683*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(3072000*Sqrt[1 - 2*x])

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IntegrateAlgebraic [A]  time = 0.24, size = 157, normalized size = 0.98 \begin {gather*} -\frac {1771561 \sqrt {1-2 x} \left (\frac {9375 (1-2 x)^5}{(5 x+3)^5}+\frac {21250 (1-2 x)^4}{(5 x+3)^4}+\frac {19800 (1-2 x)^3}{(5 x+3)^3}-\frac {7920 (1-2 x)^2}{(5 x+3)^2}-\frac {1360 (1-2 x)}{5 x+3}-96\right )}{307200 \sqrt {5 x+3} \left (\frac {5 (1-2 x)}{5 x+3}+2\right )^6}-\frac {1771561 \tan ^{-1}\left (\frac {\sqrt {\frac {5}{2}} \sqrt {1-2 x}}{\sqrt {5 x+3}}\right )}{102400 \sqrt {10}} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2),x]

[Out]

(-1771561*Sqrt[1 - 2*x]*(-96 + (9375*(1 - 2*x)^5)/(3 + 5*x)^5 + (21250*(1 - 2*x)^4)/(3 + 5*x)^4 + (19800*(1 -
2*x)^3)/(3 + 5*x)^3 - (7920*(1 - 2*x)^2)/(3 + 5*x)^2 - (1360*(1 - 2*x))/(3 + 5*x)))/(307200*Sqrt[3 + 5*x]*(2 +
(5*(1 - 2*x))/(3 + 5*x))^6) - (1771561*ArcTan[(Sqrt[5/2]*Sqrt[1 - 2*x])/Sqrt[3 + 5*x]])/(102400*Sqrt[10])

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fricas [A]  time = 1.10, size = 82, normalized size = 0.51 \begin {gather*} \frac {1}{307200} \, {\left (5120000 \, x^{5} + 1280000 \, x^{4} - 4905600 \, x^{3} - 748640 \, x^{2} + 1895020 \, x + 96003\right )} \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1} - \frac {1771561}{2048000} \, \sqrt {10} \arctan \left (\frac {\sqrt {10} {\left (20 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1}}{20 \, {\left (10 \, x^{2} + x - 3\right )}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/307200*(5120000*x^5 + 1280000*x^4 - 4905600*x^3 - 748640*x^2 + 1895020*x + 96003)*sqrt(5*x + 3)*sqrt(-2*x +
1) - 1771561/2048000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))

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giac [B]  time = 1.66, size = 356, normalized size = 2.22 \begin {gather*} \frac {1}{76800000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (8 \, {\left (4 \, {\left (16 \, {\left (100 \, x - 311\right )} {\left (5 \, x + 3\right )} + 46071\right )} {\left (5 \, x + 3\right )} - 775911\right )} {\left (5 \, x + 3\right )} + 15385695\right )} {\left (5 \, x + 3\right )} - 99422145\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} - 220189365 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} + \frac {1}{2400000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (8 \, {\left (12 \, {\left (80 \, x - 203\right )} {\left (5 \, x + 3\right )} + 19073\right )} {\left (5 \, x + 3\right )} - 506185\right )} {\left (5 \, x + 3\right )} + 4031895\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} + 10392195 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} - \frac {47}{1920000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (8 \, {\left (60 \, x - 119\right )} {\left (5 \, x + 3\right )} + 6163\right )} {\left (5 \, x + 3\right )} - 66189\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} - 184305 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} - \frac {69}{40000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (40 \, x - 59\right )} {\left (5 \, x + 3\right )} + 1293\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} + 4785 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} + \frac {27}{2000} \, \sqrt {5} {\left (2 \, {\left (20 \, x - 23\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} - 143 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} + \frac {27}{50} \, \sqrt {5} {\left (11 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right ) + 2 \, \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/76800000*sqrt(5)*(2*(4*(8*(4*(16*(100*x - 311)*(5*x + 3) + 46071)*(5*x + 3) - 775911)*(5*x + 3) + 15385695)*
(5*x + 3) - 99422145)*sqrt(5*x + 3)*sqrt(-10*x + 5) - 220189365*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) +
1/2400000*sqrt(5)*(2*(4*(8*(12*(80*x - 203)*(5*x + 3) + 19073)*(5*x + 3) - 506185)*(5*x + 3) + 4031895)*sqrt(
5*x + 3)*sqrt(-10*x + 5) + 10392195*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) - 47/1920000*sqrt(5)*(2*(4*(8
*(60*x - 119)*(5*x + 3) + 6163)*(5*x + 3) - 66189)*sqrt(5*x + 3)*sqrt(-10*x + 5) - 184305*sqrt(2)*arcsin(1/11*
sqrt(22)*sqrt(5*x + 3))) - 69/40000*sqrt(5)*(2*(4*(40*x - 59)*(5*x + 3) + 1293)*sqrt(5*x + 3)*sqrt(-10*x + 5)
+ 4785*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) + 27/2000*sqrt(5)*(2*(20*x - 23)*sqrt(5*x + 3)*sqrt(-10*x
+ 5) - 143*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) + 27/50*sqrt(5)*(11*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(
5*x + 3)) + 2*sqrt(5*x + 3)*sqrt(-10*x + 5))

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maple [A]  time = 0.00, size = 136, normalized size = 0.85 \begin {gather*} \frac {1771561 \sqrt {\left (-2 x +1\right ) \left (5 x +3\right )}\, \sqrt {10}\, \arcsin \left (\frac {20 x}{11}+\frac {1}{11}\right )}{2048000 \sqrt {5 x +3}\, \sqrt {-2 x +1}}+\frac {\left (-2 x +1\right )^{\frac {5}{2}} \left (5 x +3\right )^{\frac {7}{2}}}{30}+\frac {11 \left (-2 x +1\right )^{\frac {3}{2}} \left (5 x +3\right )^{\frac {7}{2}}}{300}+\frac {121 \left (5 x +3\right )^{\frac {7}{2}} \sqrt {-2 x +1}}{4000}-\frac {1331 \left (5 x +3\right )^{\frac {5}{2}} \sqrt {-2 x +1}}{48000}-\frac {14641 \left (5 x +3\right )^{\frac {3}{2}} \sqrt {-2 x +1}}{76800}-\frac {161051 \sqrt {-2 x +1}\, \sqrt {5 x +3}}{102400} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/30*(-2*x+1)^(5/2)*(5*x+3)^(7/2)+11/300*(-2*x+1)^(3/2)*(5*x+3)^(7/2)+121/4000*(5*x+3)^(7/2)*(-2*x+1)^(1/2)-13
31/48000*(5*x+3)^(5/2)*(-2*x+1)^(1/2)-14641/76800*(5*x+3)^(3/2)*(-2*x+1)^(1/2)-161051/102400*(-2*x+1)^(1/2)*(5
*x+3)^(1/2)+1771561/2048000*((-2*x+1)*(5*x+3))^(1/2)/(5*x+3)^(1/2)/(-2*x+1)^(1/2)*10^(1/2)*arcsin(20/11*x+1/11
)

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maxima [A]  time = 1.38, size = 99, normalized size = 0.62 \begin {gather*} \frac {1}{6} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} x + \frac {1}{120} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} + \frac {121}{192} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {3}{2}} x + \frac {121}{3840} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {3}{2}} + \frac {14641}{5120} \, \sqrt {-10 \, x^{2} - x + 3} x - \frac {1771561}{2048000} \, \sqrt {10} \arcsin \left (-\frac {20}{11} \, x - \frac {1}{11}\right ) + \frac {14641}{102400} \, \sqrt {-10 \, x^{2} - x + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/6*(-10*x^2 - x + 3)^(5/2)*x + 1/120*(-10*x^2 - x + 3)^(5/2) + 121/192*(-10*x^2 - x + 3)^(3/2)*x + 121/3840*(
-10*x^2 - x + 3)^(3/2) + 14641/5120*sqrt(-10*x^2 - x + 3)*x - 1771561/2048000*sqrt(10)*arcsin(-20/11*x - 1/11)
+ 14641/102400*sqrt(-10*x^2 - x + 3)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int {\left (1-2\,x\right )}^{5/2}\,{\left (5\,x+3\right )}^{5/2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 24.94, size = 357, normalized size = 2.23 \begin {gather*} \begin {cases} \frac {500 i \left (x + \frac {3}{5}\right )^{\frac {13}{2}}}{3 \sqrt {10 x - 5}} - \frac {1925 i \left (x + \frac {3}{5}\right )^{\frac {11}{2}}}{3 \sqrt {10 x - 5}} + \frac {40535 i \left (x + \frac {3}{5}\right )^{\frac {9}{2}}}{48 \sqrt {10 x - 5}} - \frac {73205 i \left (x + \frac {3}{5}\right )^{\frac {7}{2}}}{192 \sqrt {10 x - 5}} - \frac {14641 i \left (x + \frac {3}{5}\right )^{\frac {5}{2}}}{7680 \sqrt {10 x - 5}} - \frac {161051 i \left (x + \frac {3}{5}\right )^{\frac {3}{2}}}{30720 \sqrt {10 x - 5}} + \frac {1771561 i \sqrt {x + \frac {3}{5}}}{102400 \sqrt {10 x - 5}} - \frac {1771561 \sqrt {10} i \operatorname {acosh}{\left (\frac {\sqrt {110} \sqrt {x + \frac {3}{5}}}{11} \right )}}{1024000} & \text {for}\: \frac {10 \left |{x + \frac {3}{5}}\right |}{11} > 1 \\\frac {1771561 \sqrt {10} \operatorname {asin}{\left (\frac {\sqrt {110} \sqrt {x + \frac {3}{5}}}{11} \right )}}{1024000} - \frac {500 \left (x + \frac {3}{5}\right )^{\frac {13}{2}}}{3 \sqrt {5 - 10 x}} + \frac {1925 \left (x + \frac {3}{5}\right )^{\frac {11}{2}}}{3 \sqrt {5 - 10 x}} - \frac {40535 \left (x + \frac {3}{5}\right )^{\frac {9}{2}}}{48 \sqrt {5 - 10 x}} + \frac {73205 \left (x + \frac {3}{5}\right )^{\frac {7}{2}}}{192 \sqrt {5 - 10 x}} + \frac {14641 \left (x + \frac {3}{5}\right )^{\frac {5}{2}}}{7680 \sqrt {5 - 10 x}} + \frac {161051 \left (x + \frac {3}{5}\right )^{\frac {3}{2}}}{30720 \sqrt {5 - 10 x}} - \frac {1771561 \sqrt {x + \frac {3}{5}}}{102400 \sqrt {5 - 10 x}} & \text {otherwise} \end {cases} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Piecewise((500*I*(x + 3/5)**(13/2)/(3*sqrt(10*x - 5)) - 1925*I*(x + 3/5)**(11/2)/(3*sqrt(10*x - 5)) + 40535*I*
(x + 3/5)**(9/2)/(48*sqrt(10*x - 5)) - 73205*I*(x + 3/5)**(7/2)/(192*sqrt(10*x - 5)) - 14641*I*(x + 3/5)**(5/2
)/(7680*sqrt(10*x - 5)) - 161051*I*(x + 3/5)**(3/2)/(30720*sqrt(10*x - 5)) + 1771561*I*sqrt(x + 3/5)/(102400*s
qrt(10*x - 5)) - 1771561*sqrt(10)*I*acosh(sqrt(110)*sqrt(x + 3/5)/11)/1024000, 10*Abs(x + 3/5)/11 > 1), (17715
61*sqrt(10)*asin(sqrt(110)*sqrt(x + 3/5)/11)/1024000 - 500*(x + 3/5)**(13/2)/(3*sqrt(5 - 10*x)) + 1925*(x + 3/
5)**(11/2)/(3*sqrt(5 - 10*x)) - 40535*(x + 3/5)**(9/2)/(48*sqrt(5 - 10*x)) + 73205*(x + 3/5)**(7/2)/(192*sqrt(
5 - 10*x)) + 14641*(x + 3/5)**(5/2)/(7680*sqrt(5 - 10*x)) + 161051*(x + 3/5)**(3/2)/(30720*sqrt(5 - 10*x)) - 1
771561*sqrt(x + 3/5)/(102400*sqrt(5 - 10*x)), True))

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