3.28.18 \(\int (1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx\) [2718]

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

[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 = 0.08, 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 = {103, 159, 164, 114, 120} \begin {gather*} -\frac {50299451003 F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{4146187500 \sqrt {33}}-\frac {836091184171 E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{2073093750 \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} \end {gather*}

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 103

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 114

Int[Sqrt[(e_.) + (f_.)*(x_)]/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]), x_Symbol] :> 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] &&  !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 120

Int[1/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]*Sqrt[(e_) + (f_.)*(x_)]), x_Symbol] :> 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] && Po
sQ[-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 159

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 164

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 = 8.28, size = 119, normalized size = 0.42 \begin {gather*} \frac {-30 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x} \left (44426819351-177853891770 x-522917547750 x^2-227285730000 x^3+888419542500 x^4+1316318850000 x^5+547296750000 x^6\right )+\sqrt {2} \left (3344364736684 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )-1684482853585 F\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )\right )}{273648375000} \end {gather*}

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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Maple [A]
time = 0.10, size = 168, normalized size = 0.60

method	result	size
default	\(-\frac {\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}\, \left (492567075000000 x^{9}+1562321722500000 x^{8}+1592905277250000 x^{7}[phone] x^{6}[phone] \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-3344364736684 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-1050958443600000 x^{5}-633067124890500 x^{4}[phone] x^{3}[phone] x^{2}[phone] x -7996827483180\right )}{273648375000 \left (30 x^{3}+23 x^{2}-7 x -6\right )}\)	\(168\)
risch	\(\frac {\left (547296750000 x^{6}[phone] x^{5}[phone] x^{4}-227285730000 x^{3}-522917547750 x^{2}-177853891770 x [phone]\right ) \sqrt {3+5 x}\, \left (-1+2 x \right ) \sqrt {2+3 x}\, \sqrt {\left (1-2 x \right ) \left (2+3 x \right ) \left (3+5 x \right )}}{9121612500 \sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \sqrt {1-2 x}}+\frac {\left (\frac {2117277634217 \sqrt {66+110 x}\, \sqrt {10+15 x}\, \sqrt {55-110 x}\, \EllipticF \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{1003377375000 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {836091184171 \sqrt {66+110 x}\, \sqrt {10+15 x}\, \sqrt {55-110 x}\, \left (\frac {\EllipticE \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{15}-\frac {2 \EllipticF \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{3}\right )}{250844343750 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right ) \sqrt {\left (1-2 x \right ) \left (2+3 x \right ) \left (3+5 x \right )}}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\)	\(271\)
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \sqrt {3+5 x}\, \sqrt {2+3 x}\, \left (-60 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}\, x^{6}-\frac {1876 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}\, x^{5}}{13}-\frac {69639 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}\, x^{4}}{715}+\frac {481028 x^{3} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{19305}+\frac {17877523 x^{2} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{311850}+\frac {1976154353 x \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{101351250}-\frac {44426819351 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{9121612500}+\frac {2117277634217 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{383107725000 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {836091184171 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{95776931250 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \left (15 x^{2}+19 x +6\right )}\)	\(334\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/273648375000*(1-2*x)^(1/2)*(2+3*x)^(1/2)*(3+5*x)^(1/2)*(492567075000000*x^9+1562321722500000*x^8+1592905277
250000*x^7+33511953825000*x^6+1659881883099*2^(1/2)*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)*EllipticF(1/7*(
28+42*x)^(1/2),1/2*70^(1/2))-3344364736684*2^(1/2)*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)*EllipticE(1/7*(2
8+42*x)^(1/2),1/2*70^(1/2))-1050958443600000*x^5-633067124890500*x^4+67989068522100*x^3+162128981218890*x^2+22
684068454890*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 \begin {gather*} \text {Failed to integrate} \end {gather*}

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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Fricas [A]
time = 0.25, size = 53, normalized size = 0.19 \begin {gather*} -\frac {1}{9121612500} \, {\left (547296750000 \, x^{6} + 1316318850000 \, x^{5} + 888419542500 \, x^{4} - 227285730000 \, x^{3} - 522917547750 \, x^{2} - 177853891770 \, x + 44426819351\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \end {gather*}

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]

-1/9121612500*(547296750000*x^6 + 1316318850000*x^5 + 888419542500*x^4 - 227285730000*x^3 - 522917547750*x^2 -
177853891770*x + 44426819351)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)

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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}

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]

Exception raised: SystemError >> excessive stack use: stack is 7315 deep

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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