Integrand size = 28, antiderivative size = 219 \[ \int \frac {(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx=\frac {1284329 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{3780}+\frac {4853}{105} \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}+\frac {93}{14} \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}+\frac {5}{3} \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}+\frac {(2+3 x)^{5/2} (3+5 x)^{5/2}}{\sqrt {1-2 x}}+\frac {42696881 \sqrt {\frac {11}{3}} E\left (\arcsin \left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{18900}+\frac {1284329 \sqrt {\frac {11}{3}} \operatorname {EllipticF}\left (\arcsin \left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right ),\frac {35}{33}\right )}{18900} \]
42696881/56700*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1 /2)+1284329/56700*EllipticF(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33 ^(1/2)+(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(1/2)+5/3*(2+3*x)^(3/2)*(3+5*x) ^(5/2)*(1-2*x)^(1/2)+4853/105*(3+5*x)^(3/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)+93 /14*(3+5*x)^(5/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)+1284329/3780*(1-2*x)^(1/2)*( 2+3*x)^(1/2)*(3+5*x)^(1/2)
Result contains complex when optimal does not.
Time = 8.29 (sec) , antiderivative size = 116, normalized size of antiderivative = 0.53 \[ \int \frac {(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx=\frac {-15 \sqrt {2+3 x} \sqrt {3+5 x} \left (-2283923+1258906 x+795150 x^2+392400 x^3+94500 x^4\right )-42696881 i \sqrt {33-66 x} E\left (i \text {arcsinh}\left (\sqrt {9+15 x}\right )|-\frac {2}{33}\right )+43981210 i \sqrt {33-66 x} \operatorname {EllipticF}\left (i \text {arcsinh}\left (\sqrt {9+15 x}\right ),-\frac {2}{33}\right )}{56700 \sqrt {1-2 x}} \]
(-15*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-2283923 + 1258906*x + 795150*x^2 + 3924 00*x^3 + 94500*x^4) - (42696881*I)*Sqrt[33 - 66*x]*EllipticE[I*ArcSinh[Sqr t[9 + 15*x]], -2/33] + (43981210*I)*Sqrt[33 - 66*x]*EllipticF[I*ArcSinh[Sq rt[9 + 15*x]], -2/33])/(56700*Sqrt[1 - 2*x])
Time = 0.30 (sec) , antiderivative size = 244, normalized size of antiderivative = 1.11, number of steps used = 13, number of rules used = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.464, Rules used = {108, 27, 171, 27, 171, 27, 171, 27, 171, 27, 176, 123, 129}
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.
| \(\displaystyle \int \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{(1-2 x)^{3/2}} \, dx\) |
| \(\Big \downarrow \) 108 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\int \frac {5 (3 x+2)^{3/2} (5 x+3)^{3/2} (30 x+19)}{2 \sqrt {1-2 x}}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \int \frac {(3 x+2)^{3/2} (5 x+3)^{3/2} (30 x+19)}{\sqrt {1-2 x}}dx\) |
| \(\Big \downarrow \) 171 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (-\frac {1}{45} \int -\frac {15 \sqrt {3 x+2} (5 x+3)^{3/2} (279 x+179)}{\sqrt {1-2 x}}dx-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \int \frac {\sqrt {3 x+2} (5 x+3)^{3/2} (279 x+179)}{\sqrt {1-2 x}}dx-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 171 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (-\frac {1}{35} \int -\frac {(5 x+3)^{3/2} (58236 x+38173)}{2 \sqrt {1-2 x} \sqrt {3 x+2}}dx-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (\frac {1}{70} \int \frac {(5 x+3)^{3/2} (58236 x+38173)}{\sqrt {1-2 x} \sqrt {3 x+2}}dx-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 171 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (\frac {1}{70} \left (-\frac {1}{15} \int -\frac {3 \sqrt {5 x+3} (1284329 x+834657)}{\sqrt {1-2 x} \sqrt {3 x+2}}dx-\frac {19412}{5} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}\right )-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (\frac {1}{70} \left (\frac {1}{5} \int \frac {\sqrt {5 x+3} (1284329 x+834657)}{\sqrt {1-2 x} \sqrt {3 x+2}}dx-\frac {19412}{5} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}\right )-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 171 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (\frac {1}{70} \left (\frac {1}{5} \left (-\frac {1}{9} \int -\frac {85393762 x+54061781}{2 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}dx-\frac {1284329}{9} \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}\right )-\frac {19412}{5} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}\right )-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (\frac {1}{70} \left (\frac {1}{5} \left (\frac {1}{18} \int \frac {85393762 x+54061781}{\sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}dx-\frac {1284329}{9} \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}\right )-\frac {19412}{5} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}\right )-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 176 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (\frac {1}{70} \left (\frac {1}{5} \left (\frac {1}{18} \left (\frac {14127619}{5} \int \frac {1}{\sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}dx+\frac {85393762}{5} \int \frac {\sqrt {5 x+3}}{\sqrt {1-2 x} \sqrt {3 x+2}}dx\right )-\frac {1284329}{9} \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}\right )-\frac {19412}{5} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}\right )-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 123 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (\frac {1}{70} \left (\frac {1}{5} \left (\frac {1}{18} \left (\frac {14127619}{5} \int \frac {1}{\sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}dx-\frac {85393762}{5} \sqrt {\frac {11}{3}} E\left (\arcsin \left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )\right )-\frac {1284329}{9} \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}\right )-\frac {19412}{5} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}\right )-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
| \(\Big \downarrow \) 129 |
| \(\displaystyle \frac {(3 x+2)^{5/2} (5 x+3)^{5/2}}{\sqrt {1-2 x}}-\frac {5}{2} \left (\frac {1}{3} \left (\frac {1}{70} \left (\frac {1}{5} \left (\frac {1}{18} \left (-\frac {2568658}{5} \sqrt {\frac {11}{3}} \operatorname {EllipticF}\left (\arcsin \left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right ),\frac {35}{33}\right )-\frac {85393762}{5} \sqrt {\frac {11}{3}} E\left (\arcsin \left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )\right )-\frac {1284329}{9} \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}\right )-\frac {19412}{5} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}\right )-\frac {279}{35} \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}\right )-\frac {2}{3} \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}\right )\) |
((2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x] - (5*((-2*Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/3 + ((-279*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/35 + ((-19412*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2))/5 + ((-1284329*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/9 + ((-85393762*Sq rt[11/3]*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/5 - (2568658*S qrt[11/3]*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/5)/18)/5)/70) /3))/2
3.30.9.3.1 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_)*((e_.) + (f_.)*(x_) )^(p_), x_] :> Simp[(a + b*x)^(m + 1)*(c + d*x)^n*((e + f*x)^p/(b*(m + 1))) , x] - Simp[1/(b*(m + 1)) Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f* x)^(p - 1)*Simp[d*e*n + c*f*p + d*f*(n + p)*x, x], x], x] /; FreeQ[{a, b, c , d, e, f}, x] && LtQ[m, -1] && GtQ[n, 0] && GtQ[p, 0] && (IntegersQ[2*m, 2 *n, 2*p] || IntegersQ[m, n + p] || IntegersQ[p, m + n])
Int[Sqrt[(e_.) + (f_.)*(x_)]/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_ )]), x_] :> Simp[(2/b)*Rt[-(b*e - a*f)/d, 2]*EllipticE[ArcSin[Sqrt[a + b*x] /Rt[-(b*c - a*d)/d, 2]], f*((b*c - a*d)/(d*(b*e - a*f)))], x] /; FreeQ[{a, b, c, d, e, f}, x] && GtQ[b/(b*c - a*d), 0] && GtQ[b/(b*e - a*f), 0] && !L tQ[-(b*c - a*d)/d, 0] && !(SimplerQ[c + d*x, a + b*x] && GtQ[-d/(b*c - a*d ), 0] && GtQ[d/(d*e - c*f), 0] && !LtQ[(b*c - a*d)/b, 0])
Int[1/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]*Sqrt[(e_) + (f_.)*(x _)]), x_] :> Simp[2*(Rt[-b/d, 2]/(b*Sqrt[(b*e - a*f)/b]))*EllipticF[ArcSin[ Sqrt[a + b*x]/(Rt[-b/d, 2]*Sqrt[(b*c - a*d)/b])], f*((b*c - a*d)/(d*(b*e - a*f)))], x] /; FreeQ[{a, b, c, d, e, f}, x] && GtQ[(b*c - a*d)/b, 0] && GtQ [(b*e - a*f)/b, 0] && PosQ[-b/d] && !(SimplerQ[c + d*x, a + b*x] && GtQ[(d *e - c*f)/d, 0] && GtQ[-d/b, 0]) && !(SimplerQ[c + d*x, a + b*x] && GtQ[(( -b)*e + a*f)/f, 0] && GtQ[-f/b, 0]) && !(SimplerQ[e + f*x, a + b*x] && GtQ [((-d)*e + c*f)/f, 0] && GtQ[((-b)*e + a*f)/f, 0] && (PosQ[-f/d] || PosQ[-f /b]))
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] && IntegersQ[2*m, 2*n, 2*p]
Int[((g_.) + (h_.)*(x_))/(Sqrt[(a_.) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]* Sqrt[(e_) + (f_.)*(x_)]), x_] :> Simp[h/f Int[Sqrt[e + f*x]/(Sqrt[a + b*x ]*Sqrt[c + d*x]), x], x] + Simp[(f*g - e*h)/f Int[1/(Sqrt[a + b*x]*Sqrt[c + d*x]*Sqrt[e + f*x]), x], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x] && Sim plerQ[a + b*x, e + f*x] && SimplerQ[c + d*x, e + f*x]
Time = 1.36 (sec) , antiderivative size = 155, normalized size of antiderivative = 0.71
| method | result | size |
| default | \(\frac {\sqrt {2+3 x}\, \sqrt {3+5 x}\, \sqrt {1-2 x}\, \left (41467998 \sqrt {5}\, \sqrt {2+3 x}\, \sqrt {7}\, \sqrt {1-2 x}\, \sqrt {-3-5 x}\, F\left (\sqrt {10+15 x}, \frac {\sqrt {70}}{35}\right )-42696881 \sqrt {5}\, \sqrt {2+3 x}\, \sqrt {7}\, \sqrt {1-2 x}\, \sqrt {-3-5 x}\, E\left (\sqrt {10+15 x}, \frac {\sqrt {70}}{35}\right )+21262500 x^{6}+115222500 x^{5}+299247750 x^{4}+545187600 x^{3}-83530965 x^{2}-537616515 x -205553070\right )}{1701000 x^{3}+1304100 x^{2}-396900 x -340200}\) | \(155\) |
| elliptic | \(\frac {\sqrt {-\left (-1+2 x \right ) \left (3+5 x \right ) \left (2+3 x \right )}\, \sqrt {3+5 x}\, \sqrt {2+3 x}\, \left (\frac {22555 x \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{168}+\frac {3532787 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{15120}-\frac {54061781 \sqrt {10+15 x}\, \sqrt {21-42 x}\, \sqrt {-15 x -9}\, F\left (\sqrt {10+15 x}, \frac {\sqrt {70}}{35}\right )}{396900 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}-\frac {42696881 \sqrt {10+15 x}\, \sqrt {21-42 x}\, \sqrt {-15 x -9}\, \left (-\frac {7 E\left (\sqrt {10+15 x}, \frac {\sqrt {70}}{35}\right )}{6}+\frac {F\left (\sqrt {10+15 x}, \frac {\sqrt {70}}{35}\right )}{2}\right )}{198450 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {4885 x^{2} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{84}+\frac {25 x^{3} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{2}-\frac {5929 \left (-30 x^{2}-38 x -12\right )}{32 \sqrt {\left (x -\frac {1}{2}\right ) \left (-30 x^{2}-38 x -12\right )}}\right )}{\sqrt {1-2 x}\, \left (15 x^{2}+19 x +6\right )}\) | \(290\) |
1/56700*(2+3*x)^(1/2)*(3+5*x)^(1/2)*(1-2*x)^(1/2)*(41467998*5^(1/2)*(2+3*x )^(1/2)*7^(1/2)*(1-2*x)^(1/2)*(-3-5*x)^(1/2)*EllipticF((10+15*x)^(1/2),1/3 5*70^(1/2))-42696881*5^(1/2)*(2+3*x)^(1/2)*7^(1/2)*(1-2*x)^(1/2)*(-3-5*x)^ (1/2)*EllipticE((10+15*x)^(1/2),1/35*70^(1/2))+21262500*x^6+115222500*x^5+ 299247750*x^4+545187600*x^3-83530965*x^2-537616515*x-205553070)/(30*x^3+23 *x^2-7*x-6)
Result contains higher order function than in optimal. Order 9 vs. order 4.
Time = 0.07 (sec) , antiderivative size = 88, normalized size of antiderivative = 0.40 \[ \int \frac {(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx=\frac {675 \, {\left (94500 \, x^{4} + 392400 \, x^{3} + 795150 \, x^{2} + 1258906 \, x - 2283923\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} + 725375941 \, \sqrt {-30} {\left (2 \, x - 1\right )} {\rm weierstrassPInverse}\left (\frac {1159}{675}, \frac {38998}{91125}, x + \frac {23}{90}\right ) - 1921359645 \, \sqrt {-30} {\left (2 \, x - 1\right )} {\rm weierstrassZeta}\left (\frac {1159}{675}, \frac {38998}{91125}, {\rm weierstrassPInverse}\left (\frac {1159}{675}, \frac {38998}{91125}, x + \frac {23}{90}\right )\right )}{2551500 \, {\left (2 \, x - 1\right )}} \]
1/2551500*(675*(94500*x^4 + 392400*x^3 + 795150*x^2 + 1258906*x - 2283923) *sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1) + 725375941*sqrt(-30)*(2*x - 1 )*weierstrassPInverse(1159/675, 38998/91125, x + 23/90) - 1921359645*sqrt( -30)*(2*x - 1)*weierstrassZeta(1159/675, 38998/91125, weierstrassPInverse( 1159/675, 38998/91125, x + 23/90)))/(2*x - 1)
Timed out. \[ \int \frac {(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx=\text {Timed out} \]
\[ \int \frac {(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx=\int { \frac {{\left (5 \, x + 3\right )}^{\frac {5}{2}} {\left (3 \, x + 2\right )}^{\frac {5}{2}}}{{\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \,d x } \]
\[ \int \frac {(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx=\int { \frac {{\left (5 \, x + 3\right )}^{\frac {5}{2}} {\left (3 \, x + 2\right )}^{\frac {5}{2}}}{{\left (-2 \, x + 1\right )}^{\frac {3}{2}}} \,d x } \]
Timed out. \[ \int \frac {(2+3 x)^{5/2} (3+5 x)^{5/2}}{(1-2 x)^{3/2}} \, dx=\int \frac {{\left (3\,x+2\right )}^{5/2}\,{\left (5\,x+3\right )}^{5/2}}{{\left (1-2\,x\right )}^{3/2}} \,d x \]