3.2989 \(\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx\)

Optimal. Leaf size=249 \[ \frac{145418632 \text{EllipticF}\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right ),\frac{35}{33}\right )}{10168235 \sqrt{33}}-\frac{4839325048 \sqrt{1-2 x} \sqrt{3 x+2}}{67110351 \sqrt{5 x+3}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{499564 \sqrt{1-2 x}}{1452605 (3 x+2)^{3/2} \sqrt{5 x+3}}-\frac{2206 \sqrt{1-2 x}}{207515 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{1616}{17787 \sqrt{1-2 x} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{4839325048 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}} \]

[Out]

4/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]) + 1616/(17787*Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x
]) - (2206*Sqrt[1 - 2*x])/(207515*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]) + (499564*Sqrt[1 - 2*x])/(1452605*(2 + 3*x)^(
3/2)*Sqrt[3 + 5*x]) + (72709316*Sqrt[1 - 2*x])/(10168235*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]) - (4839325048*Sqrt[1 - 2
*x]*Sqrt[2 + 3*x])/(67110351*Sqrt[3 + 5*x]) + (4839325048*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(
10168235*Sqrt[33]) + (145418632*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(10168235*Sqrt[33])

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Rubi [A]  time = 0.100031, 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} \[ -\frac{4839325048 \sqrt{1-2 x} \sqrt{3 x+2}}{67110351 \sqrt{5 x+3}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{499564 \sqrt{1-2 x}}{1452605 (3 x+2)^{3/2} \sqrt{5 x+3}}-\frac{2206 \sqrt{1-2 x}}{207515 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{1616}{17787 \sqrt{1-2 x} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{145418632 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}}+\frac{4839325048 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

4/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]) + 1616/(17787*Sqrt[1 - 2*x]*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x
]) - (2206*Sqrt[1 - 2*x])/(207515*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x]) + (499564*Sqrt[1 - 2*x])/(1452605*(2 + 3*x)^(
3/2)*Sqrt[3 + 5*x]) + (72709316*Sqrt[1 - 2*x])/(10168235*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]) - (4839325048*Sqrt[1 - 2
*x]*Sqrt[2 + 3*x])/(67110351*Sqrt[3 + 5*x]) + (4839325048*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(
10168235*Sqrt[33]) + (145418632*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(10168235*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)^{7/2} (3+5 x)^{3/2}} \, dx &=\frac{4}{231 (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}}-\frac{2}{231} \int \frac{-\frac{269}{2}-135 x}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx\\ &=\frac{4}{231 (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{1616}{17787 \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{4 \int \frac{\frac{55457}{4}+21210 x}{\sqrt{1-2 x} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx}{17787}\\ &=\frac{4}{231 (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{1616}{17787 \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}}-\frac{2206 \sqrt{1-2 x}}{207515 (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{8 \int \frac{\frac{429823}{4}+\frac{82725 x}{4}}{\sqrt{1-2 x} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx}{622545}\\ &=\frac{4}{231 (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{1616}{17787 \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}}-\frac{2206 \sqrt{1-2 x}}{207515 (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{499564 \sqrt{1-2 x}}{1452605 (2+3 x)^{3/2} \sqrt{3+5 x}}+\frac{16 \int \frac{\frac{32051607}{8}-\frac{16860285 x}{4}}{\sqrt{1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx}{13073445}\\ &=\frac{4}{231 (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{1616}{17787 \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}}-\frac{2206 \sqrt{1-2 x}}{207515 (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{499564 \sqrt{1-2 x}}{1452605 (2+3 x)^{3/2} \sqrt{3+5 x}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{2+3 x} \sqrt{3+5 x}}+\frac{32 \int \frac{\frac{661979505}{4}-\frac{817979805 x}{8}}{\sqrt{1-2 x} \sqrt{2+3 x} (3+5 x)^{3/2}} \, dx}{91514115}\\ &=\frac{4}{231 (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{1616}{17787 \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}}-\frac{2206 \sqrt{1-2 x}}{207515 (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{499564 \sqrt{1-2 x}}{1452605 (2+3 x)^{3/2} \sqrt{3+5 x}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{2+3 x} \sqrt{3+5 x}}-\frac{4839325048 \sqrt{1-2 x} \sqrt{2+3 x}}{67110351 \sqrt{3+5 x}}-\frac{64 \int \frac{\frac{34464999645}{16}+\frac{27221203395 x}{8}}{\sqrt{1-2 x} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx}{1006655265}\\ &=\frac{4}{231 (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{1616}{17787 \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}}-\frac{2206 \sqrt{1-2 x}}{207515 (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{499564 \sqrt{1-2 x}}{1452605 (2+3 x)^{3/2} \sqrt{3+5 x}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{2+3 x} \sqrt{3+5 x}}-\frac{4839325048 \sqrt{1-2 x} \sqrt{2+3 x}}{67110351 \sqrt{3+5 x}}-\frac{72709316 \int \frac{1}{\sqrt{1-2 x} \sqrt{2+3 x} \sqrt{3+5 x}} \, dx}{10168235}-\frac{4839325048 \int \frac{\sqrt{3+5 x}}{\sqrt{1-2 x} \sqrt{2+3 x}} \, dx}{111850585}\\ &=\frac{4}{231 (1-2 x)^{3/2} (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{1616}{17787 \sqrt{1-2 x} (2+3 x)^{5/2} \sqrt{3+5 x}}-\frac{2206 \sqrt{1-2 x}}{207515 (2+3 x)^{5/2} \sqrt{3+5 x}}+\frac{499564 \sqrt{1-2 x}}{1452605 (2+3 x)^{3/2} \sqrt{3+5 x}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{2+3 x} \sqrt{3+5 x}}-\frac{4839325048 \sqrt{1-2 x} \sqrt{2+3 x}}{67110351 \sqrt{3+5 x}}+\frac{4839325048 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}}+\frac{145418632 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}}\\ \end{align*}

Mathematica [A]  time = 0.191305, size = 115, normalized size = 0.46 \[ \frac{2 \left (-2 \sqrt{2} \left (1209831262 E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )-609979405 \text{EllipticF}\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right ),-\frac{33}{2}\right )\right )-\frac{1306617762960 x^5+1263428429256 x^4-559512908172 x^3-673871013766 x^2+53503915182 x+91855922241}{(1-2 x)^{3/2} (3 x+2)^{5/2} \sqrt{5 x+3}}\right )}{335551755} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(2*(-((91855922241 + 53503915182*x - 673871013766*x^2 - 559512908172*x^3 + 1263428429256*x^4 + 1306617762960*x
^5)/((1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)*Sqrt[3 + 5*x])) - 2*Sqrt[2]*(1209831262*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[
3 + 5*x]], -33/2] - 609979405*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/335551755

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Maple [C]  time = 0.027, size = 406, normalized size = 1.6 \begin{align*} -{\frac{2}{335551755\, \left ( 2\,x-1 \right ) ^{2}}\sqrt{1-2\,x} \left ( 21959258580\,\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}-43553925432\,\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}[phone]\,\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}-36294937860\,\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}-4879835240\,\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}[phone]\,\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}-4879835240\,\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 ) [phone]\,\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]\,{x}^{5}[phone]\,{x}^{4}-559512908172\,{x}^{3}-673871013766\,{x}^{2}[phone]\,x+91855922241 \right ) \left ( 2+3\,x \right ) ^{-{\frac{5}{2}}}{\frac{1}{\sqrt{3+5\,x}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2/335551755*(1-2*x)^(1/2)*(21959258580*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)-43553925432*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)[phone]*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)-36294937860*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)-4879835240*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)[phone]*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)-4879835240*2^(1/2)*(3+5*x)^(1/2)*(2+3*x)^(1/2)*(1-2*x)^(1/2)*Ell
ipticF(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)*Elli
pticE(1/11*(66+110*x)^(1/2),1/2*I*66^(1/2))[phone]*x^5+1263428429256*x^4-559512908172*x^3-673871013766*
x^2+53503915182*x+91855922241)/(2+3*x)^(5/2)/(2*x-1)^2/(3+5*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{3}{2}}{\left (3 \, x + 2\right )}^{\frac{7}{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)^(7/2)/(3+5*x)^(3/2),x, algorithm="maxima")

[Out]

integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^(7/2)*(-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}}{16200 \, x^{9} + 38340 \, x^{8} + 19062 \, x^{7} - 19761 \, x^{6} - 20272 \, x^{5} + 399 \, x^{4} + 5544 \, x^{3} + 1112 \, x^{2} - 480 \, x - 144}, 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)^(7/2)/(3+5*x)^(3/2),x, algorithm="fricas")

[Out]

integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(16200*x^9 + 38340*x^8 + 19062*x^7 - 19761*x^6 - 20272*x^
5 + 399*x^4 + 5544*x^3 + 1112*x^2 - 480*x - 144), 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)**(7/2)/(3+5*x)**(3/2),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{3}{2}}{\left (3 \, x + 2\right )}^{\frac{7}{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)^(7/2)/(3+5*x)^(3/2),x, algorithm="giac")

[Out]

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