3.30.99 \(\int \frac {1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx\) [2999]

Optimal. Leaf size=249 \[ \frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {414 \sqrt {1-2 x}}{41503 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {488436 \sqrt {1-2 x}}{290521 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {108842540 \sqrt {1-2 x} \sqrt {2+3 x}}{9587193 (3+5 x)^{3/2}}+\frac {7231789120 \sqrt {1-2 x} \sqrt {2+3 x}}{105459123 \sqrt {3+5 x}}-\frac {1446357824 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3195731 \sqrt {33}}-\frac {43537016 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3195731 \sqrt {33}} \]

[Out]

4/231/(1-2*x)^(3/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2)-1446357824/105459123*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33
*1155^(1/2))*33^(1/2)-43537016/105459123*EllipticF(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+544/59
29/(2+3*x)^(3/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2)+414/41503*(1-2*x)^(1/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2)+488436/290521
*(1-2*x)^(1/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2)-108842540/9587193*(1-2*x)^(1/2)*(2+3*x)^(1/2)/(3+5*x)^(3/2)+7231789
120/105459123*(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 = {106, 157, 164, 114, 120} \begin {gather*} -\frac {43537016 F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3195731 \sqrt {33}}-\frac {1446357824 E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3195731 \sqrt {33}}+\frac {7231789120 \sqrt {1-2 x} \sqrt {3 x+2}}{105459123 \sqrt {5 x+3}}-\frac {108842540 \sqrt {1-2 x} \sqrt {3 x+2}}{9587193 (5 x+3)^{3/2}}+\frac {488436 \sqrt {1-2 x}}{290521 \sqrt {3 x+2} (5 x+3)^{3/2}}+\frac {414 \sqrt {1-2 x}}{41503 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac {4}{231 (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{3/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

4/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 544/(5929*Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x)^(3
/2)) + (414*Sqrt[1 - 2*x])/(41503*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (488436*Sqrt[1 - 2*x])/(290521*Sqrt[2 + 3
*x]*(3 + 5*x)^(3/2)) - (108842540*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(9587193*(3 + 5*x)^(3/2)) + (7231789120*Sqrt[1
- 2*x]*Sqrt[2 + 3*x])/(105459123*Sqrt[3 + 5*x]) - (1446357824*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33
])/(3195731*Sqrt[33]) - (43537016*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(3195731*Sqrt[33])

Rule 106

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[b*(a +
b*x)^(m + 1)*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/((m + 1)*(b*c - a*d)*(b*e - a*f))), x] + Dist[1/((m + 1)*(b*
c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[a*d*f*(m + 1) - b*(d*e*(m + n + 2) +
c*f*(m + p + 2)) - b*d*f*(m + n + p + 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && LtQ[m, -1] &&
IntegersQ[2*m, 2*n, 2*p]

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 157

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[(b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/((m + 1)*(b*c - a*d)*(b*e - a*f
))), x] + Dist[1/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[(a*d*f*
g - b*(d*e + c*f)*g + b*c*e*h)*(m + 1) - (b*g - a*h)*(d*e*(n + 1) + c*f*(p + 1)) - d*f*(b*g - a*h)*(m + n + p
+ 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && LtQ[m, -1] && 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 \frac {1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx &=\frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}-\frac {2}{231} \int \frac {-\frac {273}{2}-135 x}{(1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx\\ &=\frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {4 \int \frac {\frac {57741}{4}+21420 x}{\sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx}{17787}\\ &=\frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {414 \sqrt {1-2 x}}{41503 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {8 \int \frac {\frac {335277}{4}-\frac {46575 x}{4}}{\sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx}{373527}\\ &=\frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {414 \sqrt {1-2 x}}{41503 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {488436 \sqrt {1-2 x}}{290521 \sqrt {2+3 x} (3+5 x)^{3/2}}+\frac {16 \int \frac {\frac {29197485}{8}-\frac {16484715 x}{4}}{\sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}} \, dx}{2614689}\\ &=\frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {414 \sqrt {1-2 x}}{41503 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {488436 \sqrt {1-2 x}}{290521 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {108842540 \sqrt {1-2 x} \sqrt {2+3 x}}{9587193 (3+5 x)^{3/2}}-\frac {32 \int \frac {\frac {1186340265}{8}-\frac {734687145 x}{8}}{\sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}} \, dx}{86284737}\\ &=\frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {414 \sqrt {1-2 x}}{41503 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {488436 \sqrt {1-2 x}}{290521 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {108842540 \sqrt {1-2 x} \sqrt {2+3 x}}{9587193 (3+5 x)^{3/2}}+\frac {7231789120 \sqrt {1-2 x} \sqrt {2+3 x}}{105459123 \sqrt {3+5 x}}+\frac {64 \int \frac {\frac {30905057655}{16}[phone] x}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{949132107}\\ &=\frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {414 \sqrt {1-2 x}}{41503 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {488436 \sqrt {1-2 x}}{290521 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {108842540 \sqrt {1-2 x} \sqrt {2+3 x}}{9587193 (3+5 x)^{3/2}}+\frac {7231789120 \sqrt {1-2 x} \sqrt {2+3 x}}{105459123 \sqrt {3+5 x}}+\frac {21768508 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{3195731}+\frac {1446357824 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{35153041}\\ &=\frac {4}{231 (1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {544}{5929 \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {414 \sqrt {1-2 x}}{41503 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {488436 \sqrt {1-2 x}}{290521 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {108842540 \sqrt {1-2 x} \sqrt {2+3 x}}{9587193 (3+5 x)^{3/2}}+\frac {7231789120 \sqrt {1-2 x} \sqrt {2+3 x}}{105459123 \sqrt {3+5 x}}-\frac {1446357824 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3195731 \sqrt {33}}-\frac {43537016 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3195731 \sqrt {33}}\\ \end {align*}

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Mathematica [A]
time = 8.78, size = 114, normalized size = 0.46 \begin {gather*} \frac {2 \left (\frac {41179778225+30866656614 x-308398535118 x^2-291775464272 x^3+585919463160 x^4+650861020800 x^5}{(1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}}+2 \sqrt {2} \left (361589456 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )-181999265 F\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )\right )\right )}{105459123} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*((41179778225 + 30866656614*x - 308398535118*x^2 - 291775464272*x^3 + 585919463160*x^4 + 650861020800*x^5)/
((1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 2*Sqrt[2]*(361589456*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 +
5*x]], -33/2] - 181999265*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/105459123

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(397\) vs. \(2(185)=370\).
time = 0.10, size = 398, normalized size = 1.60

method	result	size
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \left (\frac {\left (\frac {2318}{266805} x^{2}+\frac {4772}{4002075} x -\frac {22003}{8004150}\right ) \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{\left (x^{3}+\frac {23}{30} x^{2}-\frac {7}{30} x -\frac {1}{5}\right )^{2}}+\frac {\frac {13770078004}{105459123}-\frac {14463578240}{35153041} x^{2}-\frac {5795067592}{105459123} x}{\sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {4578527060 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{738213861 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {7231789120 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{738213861 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\)	\(245\)
default	\(-\frac {2 \sqrt {1-2 x}\, \left (10775411460 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-21695367360 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}[phone] \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-16633114976 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-2514262674 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}[phone] \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-2155082292 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )[phone] \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-650861020800 x^{5}-585919463160 x^{4}[phone] x^{3}[phone] x^{2}-30866656614 x -41179778225\right )}{105459123 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}} \left (-1+2 x \right )^{2}}\)	\(398\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2/105459123*(1-2*x)^(1/2)*(10775411460*2^(1/2)*EllipticF(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x^3*(2+3*x)^(1/2)*
(-3-5*x)^(1/2)*(1-2*x)^(1/2)-21695367360*2^(1/2)*EllipticE(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x^3*(2+3*x)^(1/2)
*(-3-5*x)^(1/2)*(1-2*x)^(1/2)[phone]*2^(1/2)*EllipticF(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x^2*(2+3*x)^(1/2)
*(-3-5*x)^(1/2)*(1-2*x)^(1/2)-16633114976*2^(1/2)*EllipticE(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x^2*(2+3*x)^(1/2
)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)-2514262674*2^(1/2)*EllipticF(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x*(2+3*x)^(1/2)*
(-3-5*x)^(1/2)*(1-2*x)^(1/2)[phone]*2^(1/2)*EllipticE(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x*(2+3*x)^(1/2)*(-
3-5*x)^(1/2)*(1-2*x)^(1/2)-2155082292*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))[phone]*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))-650861020800*x^5-585919463160*x^4+291775464272*x^3+308398535118*x^2-30866656614*x-411797782
25)/(2+3*x)^(3/2)/(3+5*x)^(3/2)/(-1+2*x)^2

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

[Out]

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

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Fricas [A]
time = 0.17, size = 80, normalized size = 0.32 \begin {gather*} \frac {2 \, {\left (650861020800 \, x^{5} + 585919463160 \, x^{4} - 291775464272 \, x^{3} - 308398535118 \, x^{2} + 30866656614 \, x + 41179778225\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{105459123 \, {\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/105459123*(650861020800*x^5 + 585919463160*x^4 - 291775464272*x^3 - 308398535118*x^2 + 30866656614*x + 41179
778225)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x +
36)

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

[Out]

Exception raised: SystemError >> excessive stack use: stack is 5988 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/(1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm="giac")

[Out]

integrate(1/((5*x + 3)^(5/2)*(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 \frac {1}{{\left (1-2\,x\right )}^{5/2}\,{\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/((1 - 2*x)^(5/2)*(3*x + 2)^(5/2)*(5*x + 3)^(5/2)),x)

[Out]

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

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