3.2804 \(\int \frac {(1-2 x)^{5/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx\)

Optimal. Leaf size=222 \[ \frac {58928}{147} \sqrt {\frac {11}{3}} \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right ),\frac {35}{33}\right )+\frac {2 (1-2 x)^{3/2}}{3 (3 x+2)^{7/2} \sqrt {5 x+3}}-\frac {9795160 \sqrt {3 x+2} \sqrt {1-2 x}}{441 \sqrt {5 x+3}}+\frac {324104 \sqrt {1-2 x}}{147 \sqrt {3 x+2} \sqrt {5 x+3}}+\frac {2332 \sqrt {1-2 x}}{21 (3 x+2)^{3/2} \sqrt {5 x+3}}+\frac {104 \sqrt {1-2 x}}{9 (3 x+2)^{5/2} \sqrt {5 x+3}}+\frac {1959032}{147} \sqrt {\frac {11}{3}} E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right ) \]

[Out]

1959032/441*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+58928/441*EllipticF(1/7*21^(1/2)*(1
-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+2/3*(1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(1/2)+104/9*(1-2*x)^(1/2)/(2+3*x
)^(5/2)/(3+5*x)^(1/2)+2332/21*(1-2*x)^(1/2)/(2+3*x)^(3/2)/(3+5*x)^(1/2)+324104/147*(1-2*x)^(1/2)/(2+3*x)^(1/2)
/(3+5*x)^(1/2)-9795160/441*(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 = 222, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 6, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {98, 150, 152, 158, 113, 119} \[ \frac {2 (1-2 x)^{3/2}}{3 (3 x+2)^{7/2} \sqrt {5 x+3}}-\frac {9795160 \sqrt {3 x+2} \sqrt {1-2 x}}{441 \sqrt {5 x+3}}+\frac {324104 \sqrt {1-2 x}}{147 \sqrt {3 x+2} \sqrt {5 x+3}}+\frac {2332 \sqrt {1-2 x}}{21 (3 x+2)^{3/2} \sqrt {5 x+3}}+\frac {104 \sqrt {1-2 x}}{9 (3 x+2)^{5/2} \sqrt {5 x+3}}+\frac {58928}{147} \sqrt {\frac {11}{3}} F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )+\frac {1959032}{147} \sqrt {\frac {11}{3}} E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right ) \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(3/2)),x]

[Out]

(2*(1 - 2*x)^(3/2))/(3*(2 + 3*x)^(7/2)*Sqrt[3 + 5*x]) + (104*Sqrt[1 - 2*x])/(9*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x])
+ (2332*Sqrt[1 - 2*x])/(21*(2 + 3*x)^(3/2)*Sqrt[3 + 5*x]) + (324104*Sqrt[1 - 2*x])/(147*Sqrt[2 + 3*x]*Sqrt[3 +
5*x]) - (9795160*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(441*Sqrt[3 + 5*x]) + (1959032*Sqrt[11/3]*EllipticE[ArcSin[Sqrt
[3/7]*Sqrt[1 - 2*x]], 35/33])/147 + (58928*Sqrt[11/3]*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/147

Rule 98

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

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 150

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*(e + f*x)^(p + 1))/(b*(b*e - a*f)*(m + 1)), x] - Dist[1
/(b*(b*e - a*f)*(m + 1)), Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f*x)^p*Simp[b*c*(f*g - e*h)*(m + 1) + (
b*g - a*h)*(d*e*n + c*f*(p + 1)) + d*(b*(f*g - e*h)*(m + 1) + f*(b*g - a*h)*(n + p + 1))*x, x], x], x] /; Free
Q[{a, b, c, d, e, f, g, h, p}, x] && LtQ[m, -1] && GtQ[n, 0] && IntegersQ[2*m, 2*n, 2*p]

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 {(1-2 x)^{5/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx &=\frac {2 (1-2 x)^{3/2}}{3 (2+3 x)^{7/2} \sqrt {3+5 x}}+\frac {2}{21} \int \frac {(196-161 x) \sqrt {1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx\\ &=\frac {2 (1-2 x)^{3/2}}{3 (2+3 x)^{7/2} \sqrt {3+5 x}}+\frac {104 \sqrt {1-2 x}}{9 (2+3 x)^{5/2} \sqrt {3+5 x}}-\frac {4}{315} \int \frac {-\frac {31955}{2}+21945 x}{\sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx\\ &=\frac {2 (1-2 x)^{3/2}}{3 (2+3 x)^{7/2} \sqrt {3+5 x}}+\frac {104 \sqrt {1-2 x}}{9 (2+3 x)^{5/2} \sqrt {3+5 x}}+\frac {2332 \sqrt {1-2 x}}{21 (2+3 x)^{3/2} \sqrt {3+5 x}}-\frac {8 \int \frac {-\frac {2417415}{2}+\frac {2754675 x}{2}}{\sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx}{6615}\\ &=\frac {2 (1-2 x)^{3/2}}{3 (2+3 x)^{7/2} \sqrt {3+5 x}}+\frac {104 \sqrt {1-2 x}}{9 (2+3 x)^{5/2} \sqrt {3+5 x}}+\frac {2332 \sqrt {1-2 x}}{21 (2+3 x)^{3/2} \sqrt {3+5 x}}+\frac {324104 \sqrt {1-2 x}}{147 \sqrt {2+3 x} \sqrt {3+5 x}}-\frac {16 \int \frac {-\frac {206265675}{4}+\frac {63807975 x}{2}}{\sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}} \, dx}{46305}\\ &=\frac {2 (1-2 x)^{3/2}}{3 (2+3 x)^{7/2} \sqrt {3+5 x}}+\frac {104 \sqrt {1-2 x}}{9 (2+3 x)^{5/2} \sqrt {3+5 x}}+\frac {2332 \sqrt {1-2 x}}{21 (2+3 x)^{3/2} \sqrt {3+5 x}}+\frac {324104 \sqrt {1-2 x}}{147 \sqrt {2+3 x} \sqrt {3+5 x}}-\frac {9795160 \sqrt {1-2 x} \sqrt {2+3 x}}{441 \sqrt {3+5 x}}+\frac {32 \int \frac {-\frac {1342947375}{2}-\frac {4242528675 x}{4}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{509355}\\ &=\frac {2 (1-2 x)^{3/2}}{3 (2+3 x)^{7/2} \sqrt {3+5 x}}+\frac {104 \sqrt {1-2 x}}{9 (2+3 x)^{5/2} \sqrt {3+5 x}}+\frac {2332 \sqrt {1-2 x}}{21 (2+3 x)^{3/2} \sqrt {3+5 x}}+\frac {324104 \sqrt {1-2 x}}{147 \sqrt {2+3 x} \sqrt {3+5 x}}-\frac {9795160 \sqrt {1-2 x} \sqrt {2+3 x}}{441 \sqrt {3+5 x}}-\frac {324104}{147} \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx-\frac {1959032}{147} \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx\\ &=\frac {2 (1-2 x)^{3/2}}{3 (2+3 x)^{7/2} \sqrt {3+5 x}}+\frac {104 \sqrt {1-2 x}}{9 (2+3 x)^{5/2} \sqrt {3+5 x}}+\frac {2332 \sqrt {1-2 x}}{21 (2+3 x)^{3/2} \sqrt {3+5 x}}+\frac {324104 \sqrt {1-2 x}}{147 \sqrt {2+3 x} \sqrt {3+5 x}}-\frac {9795160 \sqrt {1-2 x} \sqrt {2+3 x}}{441 \sqrt {3+5 x}}+\frac {1959032}{147} \sqrt {\frac {11}{3}} E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )+\frac {58928}{147} \sqrt {\frac {11}{3}} F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )\\ \end {align*}

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Mathematica [A]  time = 0.35, size = 110, normalized size = 0.50 \[ \frac {2}{441} \left (-4 \sqrt {2} \left (244879 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )|-\frac {33}{2}\right )-123340 \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right ),-\frac {33}{2}\right )\right )-\frac {3 \sqrt {1-2 x} \left (132234660 x^4+348250356 x^3+343801494 x^2+150788294 x+24789615\right )}{(3 x+2)^{7/2} \sqrt {5 x+3}}\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^(9/2)*(3 + 5*x)^(3/2)),x]

[Out]

(2*((-3*Sqrt[1 - 2*x]*(24789615 + 150788294*x + 343801494*x^2 + 348250356*x^3 + 132234660*x^4))/((2 + 3*x)^(7/
2)*Sqrt[3 + 5*x]) - 4*Sqrt[2]*(244879*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 123340*EllipticF[Ar
cSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/441

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fricas [F]  time = 1.05, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (4 \, x^{2} - 4 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(5/2)/(2+3*x)^(9/2)/(3+5*x)^(3/2),x, algorithm="fricas")

[Out]

integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6075*x^7 + 27540*x^6 + 53487*x^5 + 5769
0*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288), x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (-2 \, x + 1\right )}^{\frac {5}{2}}}{{\left (5 \, x + 3\right )}^{\frac {3}{2}} {\left (3 \, x + 2\right )}^{\frac {9}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(5/2)/(2+3*x)^(9/2)/(3+5*x)^(3/2),x, algorithm="giac")

[Out]

integrate((-2*x + 1)^(5/2)/((5*x + 3)^(3/2)*(3*x + 2)^(9/2)), x)

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maple [C]  time = 0.03, size = 409, normalized size = 1.84 \[ -\frac {2 \sqrt {-2 x +1}\, \sqrt {5 x +3}\, \left (793407960 x^{5}[phone] x^{4}-26446932 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x^{3} \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x^{3} \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] x^{3}-52893864 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x^{2} \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x^{2} \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )-126674718 x^{2}-35262576 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )[phone] \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, x \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )-303627192 x -7836128 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, \EllipticE \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )+3946880 \sqrt {2}\, \sqrt {5 x +3}\, \sqrt {3 x +2}\, \sqrt {-2 x +1}\, \EllipticF \left (\frac {\sqrt {110 x +66}}{11}, \frac {i \sqrt {66}}{2}\right )-74368845\right )}{441 \left (3 x +2\right )^{\frac {7}{2}} \left (10 x^{2}+x -3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2*x+1)^(5/2)/(3*x+2)^(9/2)/(5*x+3)^(3/2),x)

[Out]

-2/441*(-2*x+1)^(1/2)*(5*x+3)^(1/2)*(13320720*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)-26446932*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)-52893864*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)-35262576*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)+3946880*2^(1/2)*(5*x+3)^(1/2)*(3*x+2)^(1/2)*(-2*x+1)^(1/2)*Ellipt
icF(1/11*(110*x+66)^(1/2),1/2*I*66^(1/2))-7836128*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+1692798156*x^4+1018057896*x^3-126674718*x^2-303627192*x-7
4368845)/(3*x+2)^(7/2)/(10*x^2+x-3)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (-2 \, x + 1\right )}^{\frac {5}{2}}}{{\left (5 \, x + 3\right )}^{\frac {3}{2}} {\left (3 \, x + 2\right )}^{\frac {9}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(5/2)/(2+3*x)^(9/2)/(3+5*x)^(3/2),x, algorithm="maxima")

[Out]

integrate((-2*x + 1)^(5/2)/((5*x + 3)^(3/2)*(3*x + 2)^(9/2)), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {{\left (1-2\,x\right )}^{5/2}}{{\left (3\,x+2\right )}^{9/2}\,{\left (5\,x+3\right )}^{3/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1 - 2*x)^(5/2)/((3*x + 2)^(9/2)*(5*x + 3)^(3/2)),x)

[Out]

int((1 - 2*x)^(5/2)/((3*x + 2)^(9/2)*(5*x + 3)^(3/2)), 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((1-2*x)**(5/2)/(2+3*x)**(9/2)/(3+5*x)**(3/2),x)

[Out]

Timed out

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