3.2764 \(\int (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx\)

Optimal. Leaf size=280 \[ -\frac {13267820528 \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right ),\frac {35}{33}\right )}{5182734375 \sqrt {33}}+\frac {2}{75} (1-2 x)^{5/2} (3 x+2)^{5/2} (5 x+3)^{5/2}+\frac {62 (1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{5/2}}{2925}+\frac {3698 \sqrt {1-2 x} (3 x+2)^{5/2} (5 x+3)^{5/2}}{482625}+\frac {142391 \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{7239375}-\frac {569519 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}}{28153125}-\frac {400516993 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}}{2533781250}-\frac {13267820528 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}{11402015625}-\frac {1764163292393 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{20730937500 \sqrt {33}} \]

[Out]

62/2925*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+2/75*(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)-1764163292393
/684120937500*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-13267820528/171030234375*Elliptic
F(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+142391/7239375*(2+3*x)^(3/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2
)+3698/482625*(2+3*x)^(5/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2)-400516993/2533781250*(3+5*x)^(3/2)*(1-2*x)^(1/2)*(2+3*
x)^(1/2)-569519/28153125*(3+5*x)^(5/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)-13267820528/11402015625*(1-2*x)^(1/2)*(2+3*
x)^(1/2)*(3+5*x)^(1/2)

________________________________________________________________________________________

Rubi [A]  time = 0.12, antiderivative size = 280, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 5, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {101, 154, 158, 113, 119} \[ \frac {2}{75} (1-2 x)^{5/2} (3 x+2)^{5/2} (5 x+3)^{5/2}+\frac {62 (1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{5/2}}{2925}+\frac {3698 \sqrt {1-2 x} (3 x+2)^{5/2} (5 x+3)^{5/2}}{482625}+\frac {142391 \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{5/2}}{7239375}-\frac {569519 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}}{28153125}-\frac {400516993 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}}{2533781250}-\frac {13267820528 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}{11402015625}-\frac {13267820528 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{5182734375 \sqrt {33}}-\frac {1764163292393 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{20730937500 \sqrt {33}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-13267820528*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/11402015625 - (400516993*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*
(3 + 5*x)^(3/2))/2533781250 - (569519*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/28153125 + (142391*Sqrt[1 -
2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(5/2))/7239375 + (3698*Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/482625 +
(62*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/2925 + (2*(1 - 2*x)^(5/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2
))/75 - (1764163292393*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(20730937500*Sqrt[33]) - (1326782052
8*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(5182734375*Sqrt[33])

Rule 101

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

Rule 113

Int[Sqrt[(e_.) + (f_.)*(x_)]/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]), x_Symbol] :> Simp[(2*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))])/b, x
] /; FreeQ[{a, b, c, d, e, f}, x] && GtQ[b/(b*c - a*d), 0] && GtQ[b/(b*e - a*f), 0] &&  !LtQ[-((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])

Rule 119

Int[1/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]*Sqrt[(e_) + (f_.)*(x_)]), x_Symbol] :> Simp[(2*Rt[-(b/d
), 2]*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))])/(
b*Sqrt[(b*e - a*f)/b]), 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)]))

Rule 154

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[(h*(a + b*x)^m*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/(d*f*(m + n + p + 2)), x] + Dist[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] /; FreeQ[{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]

Rule 158

Int[((g_.) + (h_.)*(x_))/(Sqrt[(a_.) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]*Sqrt[(e_) + (f_.)*(x_)]), x_Symbol]
:> Dist[h/f, Int[Sqrt[e + f*x]/(Sqrt[a + b*x]*Sqrt[c + d*x]), x], x] + Dist[(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] && SimplerQ[a + b*x, e + f*x] &&
SimplerQ[c + d*x, e + f*x]

Rubi steps

\begin {align*} \int (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx &=\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}-\frac {2}{75} \int \left (-\frac {115}{2}-\frac {155 x}{2}\right ) (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx\\ &=\frac {62 (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}}{2925}+\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}-\frac {4 \int \left (-3320-\frac {9245 x}{4}\right ) \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2} \, dx}{14625}\\ &=\frac {3698 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}}{482625}+\frac {62 (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}}{2925}+\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}-\frac {8 \int \frac {(2+3 x)^{3/2} (3+5 x)^{3/2} \left (-\frac {1423865}{8}+\frac {2135865 x}{8}\right )}{\sqrt {1-2 x}} \, dx}{2413125}\\ &=\frac {142391 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}}{7239375}+\frac {3698 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}}{482625}+\frac {62 (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}}{2925}+\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}+\frac {8 \int \frac {\sqrt {2+3 x} (3+5 x)^{3/2} \left (\frac {117464475}{16}+\frac {76885065 x}{8}\right )}{\sqrt {1-2 x}} \, dx}{108590625}\\ &=-\frac {569519 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{28153125}+\frac {142391 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}}{7239375}+\frac {3698 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}}{482625}+\frac {62 (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}}{2925}+\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}-\frac {8 \int \frac {\left (-\frac {11836111305}{16}-\frac {18023264685 x}{16}\right ) (3+5 x)^{3/2}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{3800671875}\\ &=-\frac {400516993 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{2533781250}-\frac {569519 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{28153125}+\frac {142391 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}}{7239375}+\frac {3698 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}}{482625}+\frac {62 (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}}{2925}+\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}+\frac {8 \int \frac {\sqrt {3+5 x} \left (\frac {1551878163945}{32}[phone] x\right )}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{57010078125}\\ &=-\frac {13267820528 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{11402015625}-\frac {400516993 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{2533781250}-\frac {569519 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{28153125}+\frac {142391 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}}{7239375}+\frac {3698 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}}{482625}+\frac {62 (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}}{2925}+\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}-\frac {8 \int \frac {-\frac {50259437359155}{32}-\frac {79387348157685 x}{32}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{513090703125}\\ &=-\frac {13267820528 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{11402015625}-\frac {400516993 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{2533781250}-\frac {569519 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{28153125}+\frac {142391 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}}{7239375}+\frac {3698 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}}{482625}+\frac {62 (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}}{2925}+\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}+\frac {6633910264 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{5182734375}+\frac {1764163292393 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{228040312500}\\ &=-\frac {13267820528 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{11402015625}-\frac {400516993 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{2533781250}-\frac {569519 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{28153125}+\frac {142391 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}}{7239375}+\frac {3698 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}}{482625}+\frac {62 (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}}{2925}+\frac {2}{75} (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}-\frac {1764163292393 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{20730937500 \sqrt {33}}-\frac {13267820528 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{5182734375 \sqrt {33}}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.36, size = 119, normalized size = 0.42 \[ \frac {\sqrt {2} \left (1764163292393 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )|-\frac {33}{2}\right )-888487137545 \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right ),-\frac {33}{2}\right )\right )+30 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3} \left (547296750000 x^6+621672975000 x^5-336683182500 x^4-528977216250 x^3+48836706750 x^2+173484591165 x+12155574323\right )}{684120937500} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(12155574323 + 173484591165*x + 48836706750*x^2 - 528977216250*x
^3 - 336683182500*x^4 + 621672975000*x^5 + 547296750000*x^6) + Sqrt[2]*(1764163292393*EllipticE[ArcSin[Sqrt[2/
11]*Sqrt[3 + 5*x]], -33/2] - 888487137545*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/684120937500

________________________________________________________________________________________

fricas [F]  time = 0.84, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (5 \, x + 3\right )}^{\frac {3}{2}} {\left (3 \, x + 2\right )}^{\frac {5}{2}} {\left (-2 \, x + 1\right )}^{\frac {5}{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maple [C]  time = 0.01, size = 170, normalized size = 0.61 \[ \frac {\sqrt {-2 x +1}\, \sqrt {3 x +2}\, \sqrt {5 x +3}\, \left (492567075000000 x^{9}[phone] x^{8}[phone] x^{7}-937455630300000 x^{6}-362238910312500 x^{5}[phone] x^{4}[phone] x^{3}-36835025076780 x^{2}-33779897017530 x -1764163292393 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )-2188003378140\right )}{20523628125000 x^{3}[phone] x^{2}-4788846562500 x -4104725625000} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/684120937500*(-2*x+1)^(1/2)*(3*x+2)^(1/2)*(5*x+3)^(1/2)*(492567075000000*x^9+937140435000000*x^8+11007171000
000*x^7-937455630300000*x^6+888487137545*2^(1/2)*(5*x+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)*EllipticF(1/11*(11
0*x+66)^(1/2),1/2*I*66^(1/2))-1764163292393*2^(1/2)*(5*x+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)*EllipticE(1/11*
(110*x+66)^(1/2),1/2*I*66^(1/2))-362238910312500*x^5+361521647968500*x^4+215604575302050*x^3-36835025076780*x^
2-33779897017530*x-2188003378140)/(30*x^3+23*x^2-7*x-6)

________________________________________________________________________________________

maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (5 \, x + 3\right )}^{\frac {3}{2}} {\left (3 \, x + 2\right )}^{\frac {5}{2}} {\left (-2 \, x + 1\right )}^{\frac {5}{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

________________________________________________________________________________________