3.2944 \(\int \frac {1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx\)

Optimal. Leaf size=249 \[ -\frac {363103712 \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right ),\frac {35}{33}\right )}{1452605 \sqrt {33}}+\frac {12071114168 \sqrt {1-2 x} \sqrt {3 x+2}}{9587193 \sqrt {5 x+3}}-\frac {181551856 \sqrt {1-2 x} \sqrt {3 x+2}}{871563 (5 x+3)^{3/2}}+\frac {4115652 \sqrt {1-2 x}}{132055 \sqrt {3 x+2} (5 x+3)^{3/2}}+\frac {19548 \sqrt {1-2 x}}{18865 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (3 x+2)^{5/2} (5 x+3)^{3/2}}+\frac {4}{77 \sqrt {1-2 x} (3 x+2)^{5/2} (5 x+3)^{3/2}}-\frac {12071114168 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{1452605 \sqrt {33}} \]

[Out]

-12071114168/47935965*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-363103712/47935965*Ellipt
icF(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+4/77/(2+3*x)^(5/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2)+138/26
95*(1-2*x)^(1/2)/(2+3*x)^(5/2)/(3+5*x)^(3/2)+19548/18865*(1-2*x)^(1/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2)+4115652/132
055*(1-2*x)^(1/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2)-181551856/871563*(1-2*x)^(1/2)*(2+3*x)^(1/2)/(3+5*x)^(3/2)+12071
114168/9587193*(1-2*x)^(1/2)*(2+3*x)^(1/2)/(3+5*x)^(1/2)

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Rubi [A]  time = 0.10, 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 = {104, 152, 158, 113, 119} \[ \frac {12071114168 \sqrt {1-2 x} \sqrt {3 x+2}}{9587193 \sqrt {5 x+3}}-\frac {181551856 \sqrt {1-2 x} \sqrt {3 x+2}}{871563 (5 x+3)^{3/2}}+\frac {4115652 \sqrt {1-2 x}}{132055 \sqrt {3 x+2} (5 x+3)^{3/2}}+\frac {19548 \sqrt {1-2 x}}{18865 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (3 x+2)^{5/2} (5 x+3)^{3/2}}+\frac {4}{77 \sqrt {1-2 x} (3 x+2)^{5/2} (5 x+3)^{3/2}}-\frac {363103712 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{1452605 \sqrt {33}}-\frac {12071114168 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{1452605 \sqrt {33}} \]

Antiderivative was successfully verified.

[In]

Int[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]

[Out]

4/(77*Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (138*Sqrt[1 - 2*x])/(2695*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/
2)) + (19548*Sqrt[1 - 2*x])/(18865*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + (4115652*Sqrt[1 - 2*x])/(132055*Sqrt[2 +
3*x]*(3 + 5*x)^(3/2)) - (181551856*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(871563*(3 + 5*x)^(3/2)) + (12071114168*Sqrt[
1 - 2*x]*Sqrt[2 + 3*x])/(9587193*Sqrt[3 + 5*x]) - (12071114168*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/3
3])/(1452605*Sqrt[33]) - (363103712*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(1452605*Sqrt[33])

Rule 104

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 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 152

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 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 \frac {1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx &=\frac {4}{77 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}}-\frac {2}{77} \int \frac {-\frac {203}{2}-135 x}{\sqrt {1-2 x} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx\\ &=\frac {4}{77 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (2+3 x)^{5/2} (3+5 x)^{3/2}}-\frac {4 \int \frac {-\frac {3277}{2}+\frac {2415 x}{2}}{\sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx}{2695}\\ &=\frac {4}{77 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {19548 \sqrt {1-2 x}}{18865 (2+3 x)^{3/2} (3+5 x)^{3/2}}-\frac {8 \int \frac {-\frac {540213}{4}+\frac {366525 x}{2}}{\sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx}{56595}\\ &=\frac {4}{77 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {19548 \sqrt {1-2 x}}{18865 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {4115652 \sqrt {1-2 x}}{132055 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {16 \int \frac {-\frac {40301295}{4}+\frac {46301085 x}{4}}{\sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}} \, dx}{396165}\\ &=\frac {4}{77 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {19548 \sqrt {1-2 x}}{18865 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {4115652 \sqrt {1-2 x}}{132055 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {181551856 \sqrt {1-2 x} \sqrt {2+3 x}}{871563 (3+5 x)^{3/2}}+\frac {32 \int \frac {-\frac {3301192785}{8}+\frac {510614595 x}{2}}{\sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}} \, dx}{13073445}\\ &=\frac {4}{77 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {19548 \sqrt {1-2 x}}{18865 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {4115652 \sqrt {1-2 x}}{132055 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {181551856 \sqrt {1-2 x} \sqrt {2+3 x}}{871563 (3+5 x)^{3/2}}+\frac {12071114168 \sqrt {1-2 x} \sqrt {2+3 x}}{9587193 \sqrt {3+5 x}}-\frac {64 \int \frac {-\frac {42986714535}{8}-\frac {67900017195 x}{8}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{143807895}\\ &=\frac {4}{77 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {19548 \sqrt {1-2 x}}{18865 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {4115652 \sqrt {1-2 x}}{132055 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {181551856 \sqrt {1-2 x} \sqrt {2+3 x}}{871563 (3+5 x)^{3/2}}+\frac {12071114168 \sqrt {1-2 x} \sqrt {2+3 x}}{9587193 \sqrt {3+5 x}}+\frac {181551856 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{1452605}+\frac {12071114168 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{15978655}\\ &=\frac {4}{77 \sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {138 \sqrt {1-2 x}}{2695 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {19548 \sqrt {1-2 x}}{18865 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {4115652 \sqrt {1-2 x}}{132055 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {181551856 \sqrt {1-2 x} \sqrt {2+3 x}}{871563 (3+5 x)^{3/2}}+\frac {12071114168 \sqrt {1-2 x} \sqrt {2+3 x}}{9587193 \sqrt {3+5 x}}-\frac {12071114168 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{1452605 \sqrt {33}}-\frac {363103712 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{1452605 \sqrt {33}}\\ \end {align*}

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Mathematica [A]  time = 0.39, size = 114, normalized size = 0.46 \[ \frac {2 \left (4 \sqrt {2} \left (1508889271 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )|-\frac {33}{2}\right )-759987865 \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right ),-\frac {33}{2}\right )\right )+\frac {-8148002063400 x^5-16841199826980 x^4-9658241620704 x^3+1466692421066 x^2+2920885694212 x+687365548973}{\sqrt {1-2 x} (3 x+2)^{5/2} (5 x+3)^{3/2}}\right )}{47935965} \]

Antiderivative was successfully verified.

[In]

Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]

[Out]

(2*((687365548973 + 2920885694212*x + 1466692421066*x^2 - 9658241620704*x^3 - 16841199826980*x^4 - 81480020634
00*x^5)/(Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + 4*Sqrt[2]*(1508889271*EllipticE[ArcSin[Sqrt[2/11]*Sq
rt[3 + 5*x]], -33/2] - 759987865*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/47935965

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fricas [F]  time = 0.86, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{40500 \, x^{9} + 140400 \, x^{8} + 175365 \, x^{7} + 66873 \, x^{6} - 46885 \, x^{5} - 52853 \, x^{4} - 11968 \, x^{3} + 5112 \, x^{2} + 3024 \, x + 432}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm="fricas")

[Out]

integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(40500*x^9 + 140400*x^8 + 175365*x^7 + 66873*x^6 - 46885*x
^5 - 52853*x^4 - 11968*x^3 + 5112*x^2 + 3024*x + 432), x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (5 \, x + 3\right )}^{\frac {5}{2}} {\left (3 \, x + 2\right )}^{\frac {7}{2}} {\left (-2 \, x + 1\right )}^{\frac {3}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm="giac")

[Out]

integrate(1/((5*x + 3)^(5/2)*(3*x + 2)^(7/2)*(-2*x + 1)^(3/2)), x)

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maple [C]  time = 0.03, size = 406, normalized size = 1.63 \[ \frac {2 \sqrt {-2 x +1}\, \left (8148002063400 x^{5}[phone] x^{4}-271600068780 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x^{3} \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x^{3} \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] x^{3}-525093466308 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x^{2} \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x^{2} \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )-1466692421066 x^{2}-337991196704 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )-2920885694212 x -72426685008 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )-687365548973\right )}{47935965 \left (3 x +2\right )^{\frac {5}{2}} \left (5 x +3\right )^{\frac {3}{2}} \left (2 x -1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(-2*x+1)^(3/2)/(3*x+2)^(7/2)/(5*x+3)^(5/2),x)

[Out]

2/47935965*(-2*x+1)^(1/2)*(136797815700*2^(1/2)*EllipticF(1/11*(110*x+66)^(1/2),1/2*I*66^(1/2))*x^3*(5*x+3)^(1
/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)-271600068780*2^(1/2)*EllipticE(1/11*(110*x+66)^(1/2),1/2*I*66^(1/2))*x^3*(5*x
+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)[phone]*2^(1/2)*EllipticF(1/11*(110*x+66)^(1/2),1/2*I*66^(1/2))*x^
2*(5*x+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)-525093466308*2^(1/2)*EllipticE(1/11*(110*x+66)^(1/2),1/2*I*66^(1/
2))*x^2*(5*x+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)[phone]*2^(1/2)*EllipticF(1/11*(110*x+66)^(1/2),1/2*I*
66^(1/2))*x*(5*x+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)-337991196704*2^(1/2)*EllipticE(1/11*(110*x+66)^(1/2),1/
2*I*66^(1/2))*x*(5*x+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)[phone]*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))-72426685008*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))[phone]*x^5+16841199826980*x^4+965824162070
4*x^3-1466692421066*x^2-2920885694212*x-687365548973)/(3*x+2)^(5/2)/(5*x+3)^(3/2)/(2*x-1)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (5 \, x + 3\right )}^{\frac {5}{2}} {\left (3 \, x + 2\right )}^{\frac {7}{2}} {\left (-2 \, x + 1\right )}^{\frac {3}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm="maxima")

[Out]

integrate(1/((5*x + 3)^(5/2)*(3*x + 2)^(7/2)*(-2*x + 1)^(3/2)), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {1}{{\left (1-2\,x\right )}^{3/2}\,{\left (3\,x+2\right )}^{7/2}\,{\left (5\,x+3\right )}^{5/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((1 - 2*x)^(3/2)*(3*x + 2)^(7/2)*(5*x + 3)^(5/2)),x)

[Out]

int(1/((1 - 2*x)^(3/2)*(3*x + 2)^(7/2)*(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/(1-2*x)**(3/2)/(2+3*x)**(7/2)/(3+5*x)**(5/2),x)

[Out]

Timed out

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