3.30.79 \(\int \frac {1}{(1-2 x)^{5/2} (2+3 x)^{7/2} \sqrt {3+5 x}} \, dx\) [2979]

Optimal. Leaf size=218 \[ \frac {4 \sqrt {3+5 x}}{231 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {1336 \sqrt {3+5 x}}{17787 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {806 \sqrt {1-2 x} \sqrt {3+5 x}}{207515 (2+3 x)^{5/2}}+\frac {349904 \sqrt {1-2 x} \sqrt {3+5 x}}{1452605 (2+3 x)^{3/2}}+\frac {26062156 \sqrt {1-2 x} \sqrt {3+5 x}}{10168235 \sqrt {2+3 x}}-\frac {26062156 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{924385 \sqrt {33}}-\frac {837304 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{924385 \sqrt {33}} \]

[Out]

-26062156/30504705*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-837304/30504705*EllipticF(1/
7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+4/231*(3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^(5/2)+1336/17787*
(3+5*x)^(1/2)/(2+3*x)^(5/2)/(1-2*x)^(1/2)-806/207515*(1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(5/2)+349904/1452605*
(1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(3/2)[phone]/10168235*(1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(1/2)

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Rubi [A]
time = 0.06, antiderivative size = 218, normalized size of antiderivative = 1.00, number of steps used = 8, 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 {837304 F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{924385 \sqrt {33}}-\frac {26062156 E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{924385 \sqrt {33}}+\frac {26062156 \sqrt {1-2 x} \sqrt {5 x+3}}{10168235 \sqrt {3 x+2}}+\frac {349904 \sqrt {1-2 x} \sqrt {5 x+3}}{1452605 (3 x+2)^{3/2}}-\frac {806 \sqrt {1-2 x} \sqrt {5 x+3}}{207515 (3 x+2)^{5/2}}+\frac {1336 \sqrt {5 x+3}}{17787 \sqrt {1-2 x} (3 x+2)^{5/2}}+\frac {4 \sqrt {5 x+3}}{231 (1-2 x)^{3/2} (3 x+2)^{5/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(4*Sqrt[3 + 5*x])/(231*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + (1336*Sqrt[3 + 5*x])/(17787*Sqrt[1 - 2*x]*(2 + 3*x)^
(5/2)) - (806*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(207515*(2 + 3*x)^(5/2)) + (349904*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(14
52605*(2 + 3*x)^(3/2)) + (26062156*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(10168235*Sqrt[2 + 3*x]) - (26062156*EllipticE
[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(924385*Sqrt[33]) - (837304*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]
], 35/33])/(924385*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)^{7/2} \sqrt {3+5 x}} \, dx &=\frac {4 \sqrt {3+5 x}}{231 (1-2 x)^{3/2} (2+3 x)^{5/2}}-\frac {2}{231} \int \frac {-\frac {229}{2}-105 x}{(1-2 x)^{3/2} (2+3 x)^{7/2} \sqrt {3+5 x}} \, dx\\ &=\frac {4 \sqrt {3+5 x}}{231 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {1336 \sqrt {3+5 x}}{17787 \sqrt {1-2 x} (2+3 x)^{5/2}}+\frac {4 \int \frac {\frac {32997}{4}+12525 x}{\sqrt {1-2 x} (2+3 x)^{7/2} \sqrt {3+5 x}} \, dx}{17787}\\ &=\frac {4 \sqrt {3+5 x}}{231 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {1336 \sqrt {3+5 x}}{17787 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {806 \sqrt {1-2 x} \sqrt {3+5 x}}{207515 (2+3 x)^{5/2}}+\frac {8 \int \frac {\frac {137259}{2}+\frac {18135 x}{4}}{\sqrt {1-2 x} (2+3 x)^{5/2} \sqrt {3+5 x}} \, dx}{622545}\\ &=\frac {4 \sqrt {3+5 x}}{231 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {1336 \sqrt {3+5 x}}{17787 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {806 \sqrt {1-2 x} \sqrt {3+5 x}}{207515 (2+3 x)^{5/2}}+\frac {349904 \sqrt {1-2 x} \sqrt {3+5 x}}{1452605 (2+3 x)^{3/2}}+\frac {16 \int \frac {\frac {14298057}{8}-984105 x}{\sqrt {1-2 x} (2+3 x)^{3/2} \sqrt {3+5 x}} \, dx}{13073445}\\ &=\frac {4 \sqrt {3+5 x}}{231 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {1336 \sqrt {3+5 x}}{17787 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {806 \sqrt {1-2 x} \sqrt {3+5 x}}{207515 (2+3 x)^{5/2}}+\frac {349904 \sqrt {1-2 x} \sqrt {3+5 x}}{1452605 (2+3 x)^{3/2}}+\frac {26062156 \sqrt {1-2 x} \sqrt {3+5 x}}{10168235 \sqrt {2+3 x}}+\frac {32 \int \frac {\frac {93140595}{4}+\frac {293199255 x}{8}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{91514115}\\ &=\frac {4 \sqrt {3+5 x}}{231 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {1336 \sqrt {3+5 x}}{17787 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {806 \sqrt {1-2 x} \sqrt {3+5 x}}{207515 (2+3 x)^{5/2}}+\frac {349904 \sqrt {1-2 x} \sqrt {3+5 x}}{1452605 (2+3 x)^{3/2}}+\frac {26062156 \sqrt {1-2 x} \sqrt {3+5 x}}{10168235 \sqrt {2+3 x}}+\frac {418652 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{924385}+\frac {26062156 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{10168235}\\ &=\frac {4 \sqrt {3+5 x}}{231 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {1336 \sqrt {3+5 x}}{17787 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {806 \sqrt {1-2 x} \sqrt {3+5 x}}{207515 (2+3 x)^{5/2}}+\frac {349904 \sqrt {1-2 x} \sqrt {3+5 x}}{1452605 (2+3 x)^{3/2}}+\frac {26062156 \sqrt {1-2 x} \sqrt {3+5 x}}{10168235 \sqrt {2+3 x}}-\frac {26062156 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{924385 \sqrt {33}}-\frac {837304 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{924385 \sqrt {33}}\\ \end {align*}

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Mathematica [A]
time = 8.29, size = 107, normalized size = 0.49 \begin {gather*} \frac {\frac {2 \sqrt {6+10 x} \left (165071409-176797172 x-914077314 x^2+513206712 x^3+1407356424 x^4\right )}{(1-2 x)^{3/2} (2+3 x)^{5/2}}[phone] E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )-24493280 F\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )}{30504705 \sqrt {2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((2*Sqrt[6 + 10*x]*(165071409 - 176797172*x - 914077314*x^2 + 513206712*x^3 + 1407356424*x^4))/((1 - 2*x)^(3/2
)*(2 + 3*x)^(5/2)) + 52124312*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 24493280*EllipticF[ArcSin[S
qrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(30504705*Sqrt[2])

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(397\) vs. \(2(162)=324\).
time = 0.17, size = 398, normalized size = 1.83

method	result	size
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \left (\frac {8 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{79233 \left (-\frac {1}{2}+x \right )^{2}}-\frac {6928 \left (-30 x^{2}-38 x -12\right )}{6100941 \sqrt {\left (-\frac {1}{2}+x \right ) \left (-30 x^{2}-38 x -12\right )}}+\frac {2 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{1715 \left (\frac {2}{3}+x \right )^{3}}+\frac {-\frac {431352}{16807} x^{2}-\frac {215676}{84035} x +\frac {647028}{84035}}{\sqrt {\left (\frac {2}{3}+x \right ) \left (-30 x^{2}-3 x +9\right )}}+\frac {48 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{1715 \left (\frac {2}{3}+x \right )^{2}}+\frac {16558328 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{42706587 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {26062156 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{42706587 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\)	\(301\)
default	\(-\frac {2 \sqrt {1-2 x}\, \left (124339644 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-234559404 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}[phone] \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-195466170 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-27631032 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}[phone] \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-27631032 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )[phone] \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-7036782120 x^{5}-6788102832 x^{4}[phone] x^{3}[phone] x^{2}-294965529 x -495214227\right )}{30504705 \left (2+3 x \right )^{\frac {5}{2}} \left (-1+2 x \right )^{2} \sqrt {3+5 x}}\)	\(398\)

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)^(1/2),x,method=_RETURNVERBOSE)

[Out]

-2/30504705*(1-2*x)^(1/2)*(124339644*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)-234559404*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)-195466170*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)-27631032*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)-27631032*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*7
0^(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
))-7036782120*x^5-6788102832*x^4+3030766434*x^3+3626217802*x^2-294965529*x-495214227)/(2+3*x)^(5/2)/(-1+2*x)^2
/(3+5*x)^(1/2)

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

[Out]

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

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Fricas [A]
time = 0.25, size = 70, normalized size = 0.32 \begin {gather*} \frac {2 \, {\left (1407356424 \, x^{4} + 513206712 \, x^{3} - 914077314 \, x^{2} - 176797172 \, x + 165071409\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{30504705 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \end {gather*}

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)^(1/2),x, algorithm="fricas")

[Out]

2/30504705*(1407356424*x^4 + 513206712*x^3 - 914077314*x^2 - 176797172*x + 165071409)*sqrt(5*x + 3)*sqrt(3*x +
2)*sqrt(-2*x + 1)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)

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

[Out]

integrate(1/(sqrt(5*x + 3)*(3*x + 2)^(7/2)*(-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 )}^{7/2}\,\sqrt {5\,x+3}} \,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)^(7/2)*(5*x + 3)^(1/2)),x)

[Out]

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

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