Integrand size = 24, antiderivative size = 147 \[ \int \frac {(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx=\frac {377748 \sqrt {1-2 x} (2+3 x)^2}{831875}-\frac {71 \sqrt {1-2 x} (2+3 x)^4}{1210 (3+5 x)^2}+\frac {7 (2+3 x)^5}{11 \sqrt {1-2 x} (3+5 x)^2}-\frac {2721 \sqrt {1-2 x} (2+3 x)^3}{66550 (3+5 x)}+\frac {63 \sqrt {1-2 x} (2492512+831375 x)}{8318750}-\frac {33873 \text {arctanh}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{4159375 \sqrt {55}} \]
-33873/228765625*arctanh(1/11*55^(1/2)*(1-2*x)^(1/2))*55^(1/2)+7/11*(2+3*x )^5/(3+5*x)^2/(1-2*x)^(1/2)+377748/831875*(2+3*x)^2*(1-2*x)^(1/2)-71/1210* (2+3*x)^4*(1-2*x)^(1/2)/(3+5*x)^2-2721/66550*(2+3*x)^3*(1-2*x)^(1/2)/(3+5* x)+63/8318750*(2492512+831375*x)*(1-2*x)^(1/2)
Time = 0.16 (sec) , antiderivative size = 73, normalized size of antiderivative = 0.50 \[ \int \frac {(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx=\frac {-\frac {55 \left (-1702670584-4150263077 x+762244410 x^2+5682717810 x^3+1423105200 x^4+242574750 x^5\right )}{\sqrt {1-2 x} (3+5 x)^2}-67746 \sqrt {55} \text {arctanh}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{457531250} \]
((-55*(-1702670584 - 4150263077*x + 762244410*x^2 + 5682717810*x^3 + 14231 05200*x^4 + 242574750*x^5))/(Sqrt[1 - 2*x]*(3 + 5*x)^2) - 67746*Sqrt[55]*A rcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/457531250
Time = 0.24 (sec) , antiderivative size = 167, normalized size of antiderivative = 1.14, number of steps used = 11, number of rules used = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.417, Rules used = {109, 166, 27, 166, 27, 170, 25, 164, 73, 219}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {(3 x+2)^6}{(1-2 x)^{3/2} (5 x+3)^3} \, dx\) |
| \(\Big \downarrow \) 109 |
| \(\displaystyle \frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}-\frac {1}{11} \int \frac {(3 x+2)^4 (312 x+173)}{\sqrt {1-2 x} (5 x+3)^3}dx\) |
| \(\Big \downarrow \) 166 |
| \(\displaystyle \frac {1}{11} \left (-\frac {1}{110} \int \frac {3 (3 x+2)^3 (7219 x+4150)}{\sqrt {1-2 x} (5 x+3)^2}dx-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{11} \left (-\frac {3}{110} \int \frac {(3 x+2)^3 (7219 x+4150)}{\sqrt {1-2 x} (5 x+3)^2}dx-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
| \(\Big \downarrow \) 166 |
| \(\displaystyle \frac {1}{11} \left (-\frac {3}{110} \left (\frac {1}{55} \int \frac {7 (3 x+2)^2 (35976 x+21263)}{\sqrt {1-2 x} (5 x+3)}dx+\frac {907 \sqrt {1-2 x} (3 x+2)^3}{55 (5 x+3)}\right )-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{11} \left (-\frac {3}{110} \left (\frac {7}{55} \int \frac {(3 x+2)^2 (35976 x+21263)}{\sqrt {1-2 x} (5 x+3)}dx+\frac {907 \sqrt {1-2 x} (3 x+2)^3}{55 (5 x+3)}\right )-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
| \(\Big \downarrow \) 170 |
| \(\displaystyle \frac {1}{11} \left (-\frac {3}{110} \left (\frac {7}{55} \left (-\frac {1}{25} \int -\frac {(3 x+2) (2494125 x+1494862)}{\sqrt {1-2 x} (5 x+3)}dx-\frac {35976}{25} \sqrt {1-2 x} (3 x+2)^2\right )+\frac {907 \sqrt {1-2 x} (3 x+2)^3}{55 (5 x+3)}\right )-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle \frac {1}{11} \left (-\frac {3}{110} \left (\frac {7}{55} \left (\frac {1}{25} \int \frac {(3 x+2) (2494125 x+1494862)}{\sqrt {1-2 x} (5 x+3)}dx-\frac {35976}{25} \sqrt {1-2 x} (3 x+2)^2\right )+\frac {907 \sqrt {1-2 x} (3 x+2)^3}{55 (5 x+3)}\right )-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
| \(\Big \downarrow \) 164 |
| \(\displaystyle \frac {1}{11} \left (-\frac {3}{110} \left (\frac {7}{55} \left (\frac {1}{25} \left (-\frac {1613}{5} \int \frac {1}{\sqrt {1-2 x} (5 x+3)}dx-\frac {3}{5} \sqrt {1-2 x} (831375 x+2492512)\right )-\frac {35976}{25} \sqrt {1-2 x} (3 x+2)^2\right )+\frac {907 \sqrt {1-2 x} (3 x+2)^3}{55 (5 x+3)}\right )-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
| \(\Big \downarrow \) 73 |
| \(\displaystyle \frac {1}{11} \left (-\frac {3}{110} \left (\frac {7}{55} \left (\frac {1}{25} \left (\frac {1613}{5} \int \frac {1}{\frac {11}{2}-\frac {5}{2} (1-2 x)}d\sqrt {1-2 x}-\frac {3}{5} \sqrt {1-2 x} (831375 x+2492512)\right )-\frac {35976}{25} \sqrt {1-2 x} (3 x+2)^2\right )+\frac {907 \sqrt {1-2 x} (3 x+2)^3}{55 (5 x+3)}\right )-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
| \(\Big \downarrow \) 219 |
| \(\displaystyle \frac {1}{11} \left (-\frac {3}{110} \left (\frac {7}{55} \left (\frac {1}{25} \left (\frac {3226 \text {arctanh}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )}{5 \sqrt {55}}-\frac {3}{5} \sqrt {1-2 x} (831375 x+2492512)\right )-\frac {35976}{25} \sqrt {1-2 x} (3 x+2)^2\right )+\frac {907 \sqrt {1-2 x} (3 x+2)^3}{55 (5 x+3)}\right )-\frac {71 \sqrt {1-2 x} (3 x+2)^4}{110 (5 x+3)^2}\right )+\frac {7 (3 x+2)^5}{11 \sqrt {1-2 x} (5 x+3)^2}\) |
(7*(2 + 3*x)^5)/(11*Sqrt[1 - 2*x]*(3 + 5*x)^2) + ((-71*Sqrt[1 - 2*x]*(2 + 3*x)^4)/(110*(3 + 5*x)^2) - (3*((907*Sqrt[1 - 2*x]*(2 + 3*x)^3)/(55*(3 + 5 *x)) + (7*((-35976*Sqrt[1 - 2*x]*(2 + 3*x)^2)/25 + ((-3*Sqrt[1 - 2*x]*(249 2512 + 831375*x))/5 + (3226*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/(5*Sqrt[55] ))/25))/55))/110)/11
3.22.25.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[ {p = Denominator[m]}, Simp[p/b Subst[Int[x^(p*(m + 1) - 1)*(c - a*(d/b) + d*(x^p/b))^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] && Lt Q[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntL inearQ[a, b, c, d, m, n, x]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_), x_] :> Simp[(b*c - a*d)*(a + b*x)^(m + 1)*(c + d*x)^(n - 1)*((e + f *x)^(p + 1)/(b*(b*e - a*f)*(m + 1))), x] + Simp[1/(b*(b*e - a*f)*(m + 1)) Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 2)*(e + f*x)^p*Simp[a*d*(d*e*(n - 1) + c*f*(p + 1)) + b*c*(d*e*(m - n + 2) - c*f*(m + p + 2)) + d*(a*d*f*(n + p) + b*(d*e*(m + 1) - c*f*(m + n + p + 1)))*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && LtQ[m, -1] && GtQ[n, 1] && (IntegersQ[2*m, 2*n, 2*p] || IntegersQ[m, n + p] || IntegersQ[p, m + n])
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_) + (f_.)*(x_ ))*((g_.) + (h_.)*(x_)), x_] :> Simp[(-(a*d*f*h*(n + 2) + b*c*f*h*(m + 2) - b*d*(f*g + e*h)*(m + n + 3) - b*d*f*h*(m + n + 2)*x))*(a + b*x)^(m + 1)*(( c + d*x)^(n + 1)/(b^2*d^2*(m + n + 2)*(m + n + 3))), x] + Simp[(a^2*d^2*f*h *(n + 1)*(n + 2) + a*b*d*(n + 1)*(2*c*f*h*(m + 1) - d*(f*g + e*h)*(m + n + 3)) + b^2*(c^2*f*h*(m + 1)*(m + 2) - c*d*(f*g + e*h)*(m + 1)*(m + n + 3) + d^2*e*g*(m + n + 2)*(m + n + 3)))/(b^2*d^2*(m + n + 2)*(m + n + 3)) Int[( a + b*x)^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, e, f, g, h, m, n}, x] && NeQ[m + n + 2, 0] && NeQ[m + n + 3, 0]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_)*((g_.) + (h_.)*(x_)), x_] :> Simp[(b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^n*((e + f*x)^(p + 1)/(b*(b*e - a*f)*(m + 1))), x] - Simp[1/(b*(b*e - a*f)*(m + 1)) Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f*x)^p*Simp[b* c*(f*g - e*h)*(m + 1) + (b*g - a*h)*(d*e*n + c*f*(p + 1)) + d*(b*(f*g - e*h )*(m + 1) + f*(b*g - a*h)*(n + p + 1))*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, p}, x] && ILtQ[m, -1] && GtQ[n, 0]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_) )^(p_)*((g_.) + (h_.)*(x_)), x_] :> Simp[h*(a + b*x)^m*(c + d*x)^(n + 1)*(( e + f*x)^(p + 1)/(d*f*(m + n + p + 2))), x] + Simp[1/(d*f*(m + n + p + 2)) Int[(a + b*x)^(m - 1)*(c + d*x)^n*(e + f*x)^p*Simp[a*d*f*g*(m + n + p + 2 ) - h*(b*c*e*m + a*(d*e*(n + 1) + c*f*(p + 1))) + (b*d*f*g*(m + n + p + 2) + h*(a*d*f*m - b*(d*e*(m + n + 1) + c*f*(m + p + 1))))*x, x], x], x] /; Fre eQ[{a, b, c, d, e, f, g, h, n, p}, x] && GtQ[m, 0] && NeQ[m + n + p + 2, 0] && IntegerQ[m]
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1/(Rt[a, 2]*Rt[-b, 2]))* ArcTanh[Rt[-b, 2]*(x/Rt[a, 2])], x] /; FreeQ[{a, b}, x] && NegQ[a/b] && (Gt Q[a, 0] || LtQ[b, 0])
Time = 1.09 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.41
| method | result | size |
| risch | \(-\frac {242574750 x^{5}+1423105200 x^{4}+5682717810 x^{3}+762244410 x^{2}-4150263077 x -1702670584}{8318750 \left (3+5 x \right )^{2} \sqrt {1-2 x}}-\frac {33873 \,\operatorname {arctanh}\left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{228765625}\) | \(61\) |
| pseudoelliptic | \(-\frac {729 \left (\frac {11291 \sqrt {55}\, \left (x +\frac {3}{5}\right )^{2} \sqrt {1-2 x}\, \operatorname {arctanh}\left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right )}{88944075}+x^{5}+\frac {88 x^{4}}{15}+\frac {1757 x^{3}}{75}+\frac {25408147 x^{2}}{8085825}-\frac {4150263077 x}{242574750}-\frac {851335292}{121287375}\right )}{25 \sqrt {1-2 x}\, \left (3+5 x \right )^{2}}\) | \(70\) |
| derivativedivides | \(\frac {729 \left (1-2 x \right )^{\frac {5}{2}}}{5000}-\frac {8991 \left (1-2 x \right )^{\frac {3}{2}}}{5000}+\frac {333639 \sqrt {1-2 x}}{25000}+\frac {\frac {403 \left (1-2 x \right )^{\frac {3}{2}}}{831875}-\frac {81 \sqrt {1-2 x}}{75625}}{\left (-6-10 x \right )^{2}}-\frac {33873 \,\operatorname {arctanh}\left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{228765625}+\frac {117649}{10648 \sqrt {1-2 x}}\) | \(84\) |
| default | \(\frac {729 \left (1-2 x \right )^{\frac {5}{2}}}{5000}-\frac {8991 \left (1-2 x \right )^{\frac {3}{2}}}{5000}+\frac {333639 \sqrt {1-2 x}}{25000}+\frac {\frac {403 \left (1-2 x \right )^{\frac {3}{2}}}{831875}-\frac {81 \sqrt {1-2 x}}{75625}}{\left (-6-10 x \right )^{2}}-\frac {33873 \,\operatorname {arctanh}\left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{228765625}+\frac {117649}{10648 \sqrt {1-2 x}}\) | \(84\) |
| trager | \(\frac {\left (242574750 x^{5}+1423105200 x^{4}+5682717810 x^{3}+762244410 x^{2}-4150263077 x -1702670584\right ) \sqrt {1-2 x}}{8318750 \left (3+5 x \right )^{2} \left (-1+2 x \right )}-\frac {33873 \operatorname {RootOf}\left (\textit {\_Z}^{2}-55\right ) \ln \left (\frac {-5 \operatorname {RootOf}\left (\textit {\_Z}^{2}-55\right ) x +55 \sqrt {1-2 x}+8 \operatorname {RootOf}\left (\textit {\_Z}^{2}-55\right )}{3+5 x}\right )}{457531250}\) | \(94\) |
-1/8318750*(242574750*x^5+1423105200*x^4+5682717810*x^3+762244410*x^2-4150 263077*x-1702670584)/(3+5*x)^2/(1-2*x)^(1/2)-33873/228765625*arctanh(1/11* 55^(1/2)*(1-2*x)^(1/2))*55^(1/2)
Time = 0.23 (sec) , antiderivative size = 99, normalized size of antiderivative = 0.67 \[ \int \frac {(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx=\frac {33873 \, \sqrt {55} {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (\frac {5 \, x + \sqrt {55} \sqrt {-2 \, x + 1} - 8}{5 \, x + 3}\right ) + 55 \, {\left (242574750 \, x^{5} + 1423105200 \, x^{4} + 5682717810 \, x^{3} + 762244410 \, x^{2} - 4150263077 \, x - 1702670584\right )} \sqrt {-2 \, x + 1}}{457531250 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
1/457531250*(33873*sqrt(55)*(50*x^3 + 35*x^2 - 12*x - 9)*log((5*x + sqrt(5 5)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(242574750*x^5 + 1423105200*x^4 + 5 682717810*x^3 + 762244410*x^2 - 4150263077*x - 1702670584)*sqrt(-2*x + 1)) /(50*x^3 + 35*x^2 - 12*x - 9)
Timed out. \[ \int \frac {(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx=\text {Timed out} \]
Time = 0.28 (sec) , antiderivative size = 110, normalized size of antiderivative = 0.75 \[ \int \frac {(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx=\frac {729}{5000} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {8991}{5000} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {33873}{457531250} \, \sqrt {55} \log \left (-\frac {\sqrt {55} - 5 \, \sqrt {-2 \, x + 1}}{\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}}\right ) + \frac {333639}{25000} \, \sqrt {-2 \, x + 1} + \frac {1838268849 \, {\left (2 \, x - 1\right )}^{2} + 16176751756 \, x + 808829747}{6655000 \, {\left (25 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - 110 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + 121 \, \sqrt {-2 \, x + 1}\right )}} \]
729/5000*(-2*x + 1)^(5/2) - 8991/5000*(-2*x + 1)^(3/2) + 33873/457531250*s qrt(55)*log(-(sqrt(55) - 5*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) + 333639/25000*sqrt(-2*x + 1) + 1/6655000*(1838268849*(2*x - 1)^2 + 161767 51756*x + 808829747)/(25*(-2*x + 1)^(5/2) - 110*(-2*x + 1)^(3/2) + 121*sqr t(-2*x + 1))
Time = 0.29 (sec) , antiderivative size = 111, normalized size of antiderivative = 0.76 \[ \int \frac {(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx=\frac {729}{5000} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {8991}{5000} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {33873}{457531250} \, \sqrt {55} \log \left (\frac {{\left | -2 \, \sqrt {55} + 10 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}\right )}}\right ) + \frac {333639}{25000} \, \sqrt {-2 \, x + 1} + \frac {117649}{10648 \, \sqrt {-2 \, x + 1}} + \frac {403 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - 891 \, \sqrt {-2 \, x + 1}}{3327500 \, {\left (5 \, x + 3\right )}^{2}} \]
729/5000*(2*x - 1)^2*sqrt(-2*x + 1) - 8991/5000*(-2*x + 1)^(3/2) + 33873/4 57531250*sqrt(55)*log(1/2*abs(-2*sqrt(55) + 10*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) + 333639/25000*sqrt(-2*x + 1) + 117649/10648/sqrt(-2*x + 1) + 1/3327500*(403*(-2*x + 1)^(3/2) - 891*sqrt(-2*x + 1))/(5*x + 3)^2
Time = 1.43 (sec) , antiderivative size = 91, normalized size of antiderivative = 0.62 \[ \int \frac {(2+3 x)^6}{(1-2 x)^{3/2} (3+5 x)^3} \, dx=\frac {\frac {367653449\,x}{3781250}+\frac {1838268849\,{\left (2\,x-1\right )}^2}{166375000}+\frac {73529977}{15125000}}{\frac {121\,\sqrt {1-2\,x}}{25}-\frac {22\,{\left (1-2\,x\right )}^{3/2}}{5}+{\left (1-2\,x\right )}^{5/2}}+\frac {333639\,\sqrt {1-2\,x}}{25000}-\frac {8991\,{\left (1-2\,x\right )}^{3/2}}{5000}+\frac {729\,{\left (1-2\,x\right )}^{5/2}}{5000}+\frac {\sqrt {55}\,\mathrm {atan}\left (\frac {\sqrt {55}\,\sqrt {1-2\,x}\,1{}\mathrm {i}}{11}\right )\,33873{}\mathrm {i}}{228765625} \]
((367653449*x)/3781250 + (1838268849*(2*x - 1)^2)/166375000 + 73529977/151 25000)/((121*(1 - 2*x)^(1/2))/25 - (22*(1 - 2*x)^(3/2))/5 + (1 - 2*x)^(5/2 )) + (55^(1/2)*atan((55^(1/2)*(1 - 2*x)^(1/2)*1i)/11)*33873i)/228765625 + (333639*(1 - 2*x)^(1/2))/25000 - (8991*(1 - 2*x)^(3/2))/5000 + (729*(1 - 2 *x)^(5/2))/5000