3.28.64 \(\int (1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2} \, dx\) [2764]

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

[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)

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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 {13267820528 F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{5182734375 \sqrt {33}}-\frac {1764163292393 E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{20730937500 \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} \end {gather*}

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 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)^{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*}

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Mathematica [A]
time = 9.18, size = 119, normalized size = 0.42 \begin {gather*} \frac {30 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x} \left (12155574323+173484591165 x+48836706750 x^2-528977216250 x^3-336683182500 x^4+621672975000 x^5+547296750000 x^6\right )+\sqrt {2} \left (1764163292393 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )-888487137545 F\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )\right )}{684120937500} \end {gather*}

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

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

method	result	size
default	\(-\frac {\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}\, \left (-492567075000000 x^{9}-937140435000000 x^{8}-11007171000000 x^{7}[phone] x^{6}[phone] \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-1764163292393 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )[phone] x^{5}-361521647968500 x^{4}-215604575302050 x^{3}[phone] x^{2}[phone] x [phone]\right )}{684120937500 \left (30 x^{3}+23 x^{2}-7 x -6\right )}\)	\(168\)
risch	\(-\frac {\left (547296750000 x^{6}[phone] x^{5}-336683182500 x^{4}-528977216250 x^{3}[phone] x^{2}[phone] x [phone]\right ) \sqrt {3+5 x}\, \left (-1+2 x \right ) \sqrt {2+3 x}\, \sqrt {\left (1-2 x \right ) \left (2+3 x \right ) \left (3+5 x \right )}}{22804031250 \sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \sqrt {1-2 x}}-\frac {\left (-\frac {1116876385759 \sqrt {66+110 x}\, \sqrt {10+15 x}\, \sqrt {55-110 x}\, \EllipticF \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{2508443437500 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}-\frac {1764163292393 \sqrt {66+110 x}\, \sqrt {10+15 x}\, \sqrt {55-110 x}\, \left (\frac {\EllipticE \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{15}-\frac {2 \EllipticF \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{3}\right )}{2508443437500 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right ) \sqrt {\left (1-2 x \right ) \left (2+3 x \right ) \left (3+5 x \right )}}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\)	\(272\)
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \sqrt {3+5 x}\, \sqrt {2+3 x}\, \left (24 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}\, x^{6}+\frac {1772 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}\, x^{5}}{65}-\frac {52782 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}\, x^{4}}{3575}-\frac {2239057 x^{3} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{96525}+\frac {1669631 x^{2} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{779625}+\frac {3855213137 x \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{506756250}+\frac {12155574323 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{22804031250}+\frac {1116876385759 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{957769312500 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {1764163292393 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{957769312500 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \left (15 x^{2}+19 x +6\right )}\)	\(334\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/684120937500*(1-2*x)^(1/2)*(2+3*x)^(1/2)*(3+5*x)^(1/2)*(-492567075000000*x^9-937140435000000*x^8-1100717100
0000*x^7+937455630300000*x^6+875676154848*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))-1764163292393*2^(1/2)*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)*EllipticE(1/7*(28+
42*x)^(1/2),1/2*70^(1/2))[phone]*x^5-361521647968500*x^4-215604575302050*x^3+36835025076780*x^2+33779
897017530*x+2188003378140)/(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)^(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)

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Fricas [A]
time = 0.24, size = 53, normalized size = 0.19 \begin {gather*} \frac {1}{22804031250} \, {\left (547296750000 \, x^{6} + 621672975000 \, x^{5} - 336683182500 \, x^{4} - 528977216250 \, x^{3} + 48836706750 \, x^{2} + 173484591165 \, x + 12155574323\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)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2),x, algorithm="fricas")

[Out]

1/22804031250*(547296750000*x^6 + 621672975000*x^5 - 336683182500*x^4 - 528977216250*x^3 + 48836706750*x^2 + 1
73484591165*x + 12155574323)*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)**(5/2)*(2+3*x)**(5/2)*(3+5*x)**(3/2),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)^(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)

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

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)

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