3.2718 \(\int (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx\)

Optimal. Leaf size=280 \[ -\frac {50299451003 \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right ),\frac {35}{33}\right )}{4146187500 \sqrt {33}}+\frac {2}{75} (1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{7/2}+\frac {178 \sqrt {1-2 x} (3 x+2)^{5/2} (5 x+3)^{7/2}}{14625}+\frac {2503 \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{7/2}}{804375}-\frac {199721 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{7/2}}{12065625}-\frac {57509209 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}}{506756250}-\frac {380132617 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}}{506756250}-\frac {50299451003 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}{9121612500}-\frac {836091184171 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{2073093750 \sqrt {33}} \]

[Out]

2/75*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(7/2)-836091184171/68412093750*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1
/33*1155^(1/2))*33^(1/2)-50299451003/136824187500*EllipticF(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/
2)+2503/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*(1-2*x)^(1/2)+178/14625*(2+3*x)^(5/2)*(3+5*x)^(7/2)*(1-2*x)^(1/2)-3
80132617/506756250*(3+5*x)^(3/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)-57509209/506756250*(3+5*x)^(5/2)*(1-2*x)^(1/2)*(2
+3*x)^(1/2)-199721/12065625*(3+5*x)^(7/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)-50299451003/9121612500*(1-2*x)^(1/2)*(2+
3*x)^(1/2)*(3+5*x)^(1/2)

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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} \[ \frac {2}{75} (1-2 x)^{3/2} (3 x+2)^{5/2} (5 x+3)^{7/2}+\frac {178 \sqrt {1-2 x} (3 x+2)^{5/2} (5 x+3)^{7/2}}{14625}+\frac {2503 \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{7/2}}{804375}-\frac {199721 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{7/2}}{12065625}-\frac {57509209 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}}{506756250}-\frac {380132617 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}}{506756250}-\frac {50299451003 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}{9121612500}-\frac {50299451003 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{4146187500 \sqrt {33}}-\frac {836091184171 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{2073093750 \sqrt {33}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-50299451003*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/9121612500 - (380132617*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(
3 + 5*x)^(3/2))/506756250 - (57509209*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/506756250 - (199721*Sqrt[1
- 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(7/2))/12065625 + (2503*Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/804375 +
 (178*Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(7/2))/14625 + (2*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*(3 + 5*x)^(7/2
))/75 - (836091184171*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(2073093750*Sqrt[33]) - (50299451003*
EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(4146187500*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)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx &=\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {2}{75} \int \left (-\frac {71}{2}-\frac {89 x}{2}\right ) \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx\\ &=\frac {178 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}}{14625}+\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {4 \int \frac {(2+3 x)^{3/2} (3+5 x)^{5/2} \left (-\frac {2339}{2}+\frac {2503 x}{4}\right )}{\sqrt {1-2 x}} \, dx}{14625}\\ &=\frac {2503 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{804375}+\frac {178 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}}{14625}+\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}+\frac {4 \int \frac {\sqrt {2+3 x} (3+5 x)^{5/2} \left (\frac {816405}{8}+\frac {599163 x}{4}\right )}{\sqrt {1-2 x}} \, dx}{804375}\\ &=-\frac {199721 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{12065625}+\frac {2503 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{804375}+\frac {178 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}}{14625}+\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {4 \int \frac {\left (-\frac {113620371}{8}-\frac {172527627 x}{8}\right ) (3+5 x)^{5/2}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{36196875}\\ &=-\frac {57509209 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{506756250}-\frac {199721 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{12065625}+\frac {2503 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{804375}+\frac {178 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}}{14625}+\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}+\frac {4 \int \frac {(3+5 x)^{3/2} \left (\frac {22424965215}{16}+\frac {17105967765 x}{8}\right )}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{760134375}\\ &=-\frac {380132617 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{506756250}-\frac {57509209 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{506756250}-\frac {199721 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{12065625}+\frac {2503 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{804375}+\frac {178 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}}{14625}+\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {4 \int \frac {\left (-\frac {735492282165}{8}-\frac {2263475295135 x}{16}\right ) \sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{11402015625}\\ &=-\frac {50299451003 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{9121612500}-\frac {380132617 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{506756250}-\frac {57509209 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{506756250}-\frac {199721 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{12065625}+\frac {2503 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{804375}+\frac {178 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}}{14625}+\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}+\frac {4 \int \frac {\frac {95277493539765}{32}+\frac {37624103287695 x}{8}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{102618140625}\\ &=-\frac {50299451003 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{9121612500}-\frac {380132617 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{506756250}-\frac {57509209 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{506756250}-\frac {199721 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{12065625}+\frac {2503 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{804375}+\frac {178 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}}{14625}+\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}+\frac {50299451003 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{8292375000}+\frac {836091184171 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{22804031250}\\ &=-\frac {50299451003 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{9121612500}-\frac {380132617 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{506756250}-\frac {57509209 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{506756250}-\frac {199721 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{12065625}+\frac {2503 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{804375}+\frac {178 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}}{14625}+\frac {2}{75} (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {836091184171 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{2073093750 \sqrt {33}}-\frac {50299451003 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{4146187500 \sqrt {33}}\\ \end {align*}

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Mathematica [A]  time = 0.35, size = 119, normalized size = 0.42 \[ \frac {\sqrt {2} \left (3344364736684 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )|-\frac {33}{2}\right )-1684482853585 \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right ),-\frac {33}{2}\right )\right )-30 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3} \left (547296750000 x^6+1316318850000 x^5+888419542500 x^4-227285730000 x^3-522917547750 x^2-177853891770 x+44426819351\right )}{273648375000} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-30*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(44426819351 - 177853891770*x - 522917547750*x^2 - 227285730000
*x^3 + 888419542500*x^4 + 1316318850000*x^5 + 547296750000*x^6) + Sqrt[2]*(3344364736684*EllipticE[ArcSin[Sqrt
[2/11]*Sqrt[3 + 5*x]], -33/2] - 1684482853585*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2]))/27364837500
0

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fricas [F]  time = 0.93, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-{\left (450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(-(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [C]  time = 0.02, size = 170, normalized size = 0.61 \[ \frac {\sqrt {-2 x +1}\, \sqrt {3 x +2}\, \sqrt {5 x +3}\, \left (-492567075000000 x^{9}-1562321722500000 x^{8}-1592905277250000 x^{7}-33511953825000 x^{6}+1050958443600000 x^{5}+633067124890500 x^{4}-67989068522100 x^{3}-162128981218890 x^{2}-22684068454890 x -3344364736684 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )+1684482853585 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )+7996827483180\right )}{8209451250000 x^{3}+6293912625000 x^{2}-1915538625000 x -1641890250000} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/273648375000*(-2*x+1)^(1/2)*(3*x+2)^(1/2)*(5*x+3)^(1/2)*(-492567075000000*x^9-1562321722500000*x^8-159290527
7250000*x^7-33511953825000*x^6+1684482853585*2^(1/2)*(5*x+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)*EllipticF(1/11
*(110*x+66)^(1/2),1/2*I*66^(1/2))-3344364736684*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))+1050958443600000*x^5+633067124890500*x^4-67989068522100*x^3-1621289812188
90*x^2-22684068454890*x+7996827483180)/(30*x^3+23*x^2-7*x-6)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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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)**(3/2)*(2+3*x)**(5/2)*(3+5*x)**(5/2),x)

[Out]

Timed out

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