3.2999 \(\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx\)

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

[Out]

4/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/2)) + 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])

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Rubi [A]  time = 0.100295, antiderivative size = 249, normalized size of antiderivative = 1., 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} \[ \frac{7231789120 \sqrt{1-2 x} \sqrt{3 x+2}}{105459123 \sqrt{5 x+3}}-\frac{108842540 \sqrt{1-2 x} \sqrt{3 x+2}}{9587193 (5 x+3)^{3/2}}+\frac{488436 \sqrt{1-2 x}}{290521 \sqrt{3 x+2} (5 x+3)^{3/2}}+\frac{414 \sqrt{1-2 x}}{41503 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{544}{5929 \sqrt{1-2 x} (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{3/2}}-\frac{43537016 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{3195731 \sqrt{33}}-\frac{1446357824 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{3195731 \sqrt{33}} \]

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 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 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]

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)]))

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*}

Mathematica [A]  time = 0.217842, size = 114, normalized size = 0.46 \[ \frac{2 \left (2 \sqrt{2} \left (361589456 E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )-181999265 \text{EllipticF}\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right ),-\frac{33}{2}\right )\right )+\frac{650861020800 x^5+585919463160 x^4-291775464272 x^3-308398535118 x^2+30866656614 x+41179778225}{(1-2 x)^{3/2} (3 x+2)^{3/2} (5 x+3)^{3/2}}\right )}{105459123} \]

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 [C]  time = 0.026, size = 406, normalized size = 1.6 \begin{align*} -{\frac{2}{105459123\, \left ( 2\,x-1 \right ) ^{2}}\sqrt{1-2\,x} \left ( 21695367360\,\sqrt{2}{\it EllipticE} \left ( 1/11\,\sqrt{66+110\,x},i/2\sqrt{66} \right ){x}^{3}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-10919955900\,\sqrt{2}{\it EllipticF} \left ( 1/11\,\sqrt{66+110\,x},i/2\sqrt{66} \right ){x}^{3}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}[phone]\,\sqrt{2}{\it EllipticE} \left ( 1/11\,\sqrt{66+110\,x},i/2\sqrt{66} \right ){x}^{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-8371966190\,\sqrt{2}{\it EllipticF} \left ( 1/11\,\sqrt{66+110\,x},i/2\sqrt{66} \right ){x}^{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-5062252384\,\sqrt{2}{\it EllipticE} \left ( 1/11\,\sqrt{66+110\,x},i/2\sqrt{66} \right ) x\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}[phone]\,\sqrt{2}{\it EllipticF} \left ( 1/11\,\sqrt{66+110\,x},i/2\sqrt{66} \right ) x\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-4339073472\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticE} \left ( 1/11\,\sqrt{66+110\,x},i/2\sqrt{66} \right ) [phone]\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticF} \left ( 1/11\,\sqrt{66+110\,x},i/2\sqrt{66} \right ) -650861020800\,{x}^{5}-585919463160\,{x}^{4}[phone]\,{x}^{3}[phone]\,{x}^{2}-30866656614\,x-41179778225 \right ) \left ( 2+3\,x \right ) ^{-{\frac{3}{2}}} \left ( 3+5\,x \right ) ^{-{\frac{3}{2}}}} \end{align*}

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)

[Out]

-2/105459123*(1-2*x)^(1/2)*(21695367360*2^(1/2)*EllipticE(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))*x^3*(3+5*x)^(1
/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)-10919955900*2^(1/2)*EllipticF(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))*x^3*(3+5*x
)^(1/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)[phone]*2^(1/2)*EllipticE(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))*x^2*(3
+5*x)^(1/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)-8371966190*2^(1/2)*EllipticF(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))*x^2
*(3+5*x)^(1/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)-5062252384*2^(1/2)*EllipticE(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))*
x*(3+5*x)^(1/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)[phone]*2^(1/2)*EllipticF(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))
*x*(3+5*x)^(1/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)-4339073472*2^(1/2)*(3+5*x)^(1/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)*Elli
pticE(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))[phone]*2^(1/2)*(3+5*x)^(1/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)*Ellip
ticF(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))-650861020800*x^5-585919463160*x^4+291775464272*x^3+308398535118*x^2
-30866656614*x-41179778225)/(2+3*x)^(3/2)/(3+5*x)^(3/2)/(2*x-1)^2

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Maxima [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (5 \, x + 3\right )}^{\frac{5}{2}}{\left (3 \, x + 2\right )}^{\frac{5}{2}}{\left (-2 \, x + 1\right )}^{\frac{5}{2}}}\,{d x} \end{align*}

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 [F]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27000 \, x^{9} + 62100 \, x^{8} + 28710 \, x^{7} - 33013 \, x^{6} - 31539 \, x^{5} + 1419 \, x^{4} + 8693 \, x^{3} + 1602 \, x^{2} - 756 \, x - 216}, x\right ) \end{align*}

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]

integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27000*x^9 + 62100*x^8 + 28710*x^7 - 33013*x^6 - 31539*x^
5 + 1419*x^4 + 8693*x^3 + 1602*x^2 - 756*x - 216), x)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

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]

Timed out

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Giac [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (5 \, x + 3\right )}^{\frac{5}{2}}{\left (3 \, x + 2\right )}^{\frac{5}{2}}{\left (-2 \, x + 1\right )}^{\frac{5}{2}}}\,{d x} \end{align*}

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)