3.27.62 \(\int \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx\) [2662]

Optimal. Leaf size=249 \[ -\frac {493825477 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{40540500}-\frac {1865989 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{1126125}-\frac {564731 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{2252250}-\frac {2014 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{53625}-\frac {23 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{3575}+\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {16416987253 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{18427500 \sqrt {33}}-\frac {493825477 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{18427500 \sqrt {33}} \]

[Out]

-16416987253/608107500*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-493825477/608107500*Elli
pticF(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-23/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*(1-2*x)^(1/2)+2
/65*(2+3*x)^(5/2)*(3+5*x)^(7/2)*(1-2*x)^(1/2)-1865989/1126125*(3+5*x)^(3/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)-564731
/2252250*(3+5*x)^(5/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)-2014/53625*(3+5*x)^(7/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)-493825
477/40540500*(1-2*x)^(1/2)*(2+3*x)^(1/2)*(3+5*x)^(1/2)

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Rubi [A]
time = 0.07, antiderivative size = 249, normalized size of antiderivative = 1.00, number of steps used = 9, 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 {493825477 F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{18427500 \sqrt {33}}-\frac {16416987253 E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{18427500 \sqrt {33}}+\frac {2}{65} \sqrt {1-2 x} (3 x+2)^{5/2} (5 x+3)^{7/2}-\frac {23 \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{7/2}}{3575}-\frac {2014 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{7/2}}{53625}-\frac {564731 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{5/2}}{2252250}-\frac {1865989 \sqrt {1-2 x} \sqrt {3 x+2} (5 x+3)^{3/2}}{1126125}-\frac {493825477 \sqrt {1-2 x} \sqrt {3 x+2} \sqrt {5 x+3}}{40540500} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-493825477*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/40540500 - (1865989*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*
x)^(3/2))/1126125 - (564731*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/2252250 - (2014*Sqrt[1 - 2*x]*Sqrt[2
+ 3*x]*(3 + 5*x)^(7/2))/53625 - (23*Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(7/2))/3575 + (2*Sqrt[1 - 2*x]*(2
+ 3*x)^(5/2)*(3 + 5*x)^(7/2))/65 - (16416987253*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(18427500*S
qrt[33]) - (493825477*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(18427500*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 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2} \, dx &=\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {2}{65} \int \frac {\left (-\frac {27}{2}-\frac {23 x}{2}\right ) (2+3 x)^{3/2} (3+5 x)^{5/2}}{\sqrt {1-2 x}} \, dx\\ &=-\frac {23 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{3575}+\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}+\frac {2 \int \frac {\sqrt {2+3 x} (3+5 x)^{5/2} \left (\frac {7895}{4}+3021 x\right )}{\sqrt {1-2 x}} \, dx}{3575}\\ &=-\frac {2014 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{53625}-\frac {23 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{3575}+\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {2 \int \frac {\left (-278841-\frac {1694193 x}{4}\right ) (3+5 x)^{5/2}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{160875}\\ &=-\frac {564731 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{2252250}-\frac {2014 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{53625}-\frac {23 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{3575}+\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}+\frac {2 \int \frac {(3+5 x)^{3/2} \left (\frac {220162935}{8}+\frac {83969505 x}{2}\right )}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{3378375}\\ &=-\frac {1865989 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{1126125}-\frac {564731 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{2252250}-\frac {2014 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{53625}-\frac {23 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{3575}+\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {2 \int \frac {\left (-\frac {14441685345}{8}-\frac {22222146465 x}{8}\right ) \sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{50675625}\\ &=-\frac {493825477 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{40540500}-\frac {1865989 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{1126125}-\frac {564731 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{2252250}-\frac {2014 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{53625}-\frac {23 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{3575}+\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}+\frac {2 \int \frac {\frac {935406033885}{16}+\frac {738764426385 x}{8}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{456080625}\\ &=-\frac {493825477 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{40540500}-\frac {1865989 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{1126125}-\frac {564731 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{2252250}-\frac {2014 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{53625}-\frac {23 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{3575}+\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}+\frac {493825477 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{36855000}+\frac {16416987253 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{202702500}\\ &=-\frac {493825477 \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}}{40540500}-\frac {1865989 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{1126125}-\frac {564731 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}}{2252250}-\frac {2014 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{7/2}}{53625}-\frac {23 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{7/2}}{3575}+\frac {2}{65} \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{7/2}-\frac {16416987253 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{18427500 \sqrt {33}}-\frac {493825477 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{18427500 \sqrt {33}}\\ \end {align*}

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Mathematica [A]
time = 5.11, size = 112, normalized size = 0.45 \begin {gather*} \frac {15 \sqrt {2-4 x} \sqrt {2+3 x} \sqrt {3+5 x} \left (-707313559+139824180 x+2626854750 x^2+5075689500 x^3+4299277500 x^4+1403325000 x^5\right )[phone] E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )-16537733765 F\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )}{608107500 \sqrt {2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(15*Sqrt[2 - 4*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(-707313559 + 139824180*x + 2626854750*x^2 + 5075689500*x^3 + 42
99277500*x^4 + 1403325000*x^5) + 32833974506*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 16537733765*
EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(608107500*Sqrt[2])

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Maple [A]
time = 0.10, size = 163, normalized size = 0.65

method	result	size
default	\(-\frac {\sqrt {2+3 x}\, \sqrt {3+5 x}\, \sqrt {1-2 x}\, \left (-1262992500000 x^{8}-4837644000000 x^{7}-7239923775000 x^{6}[phone] \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-32833974506 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-4710948255000 x^{5}-98606794500 x^{4}[phone] x^{3}[phone] x^{2}-123367494990 x -127316440620\right )}{1216215000 \left (30 x^{3}+23 x^{2}-7 x -6\right )}\)	\(163\)
risch	\(-\frac {\left (1403325000 x^{5}[phone] x^{4}[phone] x^{3}[phone] x^{2}[phone] x -707313559\right ) \sqrt {3+5 x}\, \left (-1+2 x \right ) \sqrt {2+3 x}\, \sqrt {\left (1-2 x \right ) \left (2+3 x \right ) \left (3+5 x \right )}}{40540500 \sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \sqrt {1-2 x}}-\frac {\left (-\frac {20786800753 \sqrt {66+110 x}\, \sqrt {10+15 x}\, \sqrt {55-110 x}\, \EllipticF \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{4459455000 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}-\frac {16416987253 \sqrt {66+110 x}\, \sqrt {10+15 x}\, \sqrt {55-110 x}\, \left (\frac {\EllipticE \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{15}-\frac {2 \EllipticF \left (\frac {\sqrt {66+110 x}}{11}, \frac {i \sqrt {66}}{2}\right )}{3}\right )}{2229727500 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right ) \sqrt {\left (1-2 x \right ) \left (2+3 x \right ) \left (3+5 x \right )}}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\)	\(267\)
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \sqrt {3+5 x}\, \sqrt {2+3 x}\, \left (\frac {450 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}\, x^{5}}{13}+\frac {15165 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}\, x^{4}}{143}+\frac {53711 x^{3} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{429}+\frac {89807 x^{2} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{1386}+\frac {776801 x \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{225225}-\frac {707313559 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{40540500}+\frac {20786800753 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{1702701000 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {16416987253 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{851350500 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \left (15 x^{2}+19 x +6\right )}\)	\(312\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/1216215000*(2+3*x)^(1/2)*(3+5*x)^(1/2)*(1-2*x)^(1/2)*(-1262992500000*x^8-4837644000000*x^7-7239923775000*x^
6+16296240741*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))-3
2833974506*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))-4710
948255000*x^5-98606794500*x^4+2005367126400*x^3+990243288510*x^2-123367494990*x-127316440620)/(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((2+3*x)^(5/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm="maxima")

[Out]

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

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Fricas [A]
time = 0.11, size = 48, normalized size = 0.19 \begin {gather*} \frac {1}{40540500} \, {\left (1403325000 \, x^{5} + 4299277500 \, x^{4} + 5075689500 \, x^{3} + 2626854750 \, x^{2} + 139824180 \, x - 707313559\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((2+3*x)^(5/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm="fricas")

[Out]

1/40540500*(1403325000*x^5 + 4299277500*x^4 + 5075689500*x^3 + 2626854750*x^2 + 139824180*x - 707313559)*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((2+3*x)**(5/2)*(3+5*x)**(5/2)*(1-2*x)**(1/2),x)

[Out]

Exception raised: SystemError >> excessive stack use: stack is 4845 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((2+3*x)^(5/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm="giac")

[Out]

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

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

[Out]

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

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