3.30.7 \(\int \frac {(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{9/2}} \, dx\) [2907]

Optimal. Leaf size=222 \[ \frac {11 \sqrt {3+5 x}}{7 \sqrt {1-2 x} (2+3 x)^{7/2}}-\frac {229 \sqrt {1-2 x} \sqrt {3+5 x}}{343 (2+3 x)^{7/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{12005 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{84035 (2+3 x)^{3/2}}+\frac {189368 \sqrt {1-2 x} \sqrt {3+5 x}}{588245 \sqrt {2+3 x}}-\frac {189368 \sqrt {\frac {11}{3}} E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{588245}-\frac {23012 \sqrt {\frac {11}{3}} F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{588245} \]

[Out]

-189368/1764735*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-23012/1764735*EllipticF(1/7*21^
(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+11/7*(3+5*x)^(1/2)/(2+3*x)^(7/2)/(1-2*x)^(1/2)-229/343*(1-2*x)^(
1/2)*(3+5*x)^(1/2)/(2+3*x)^(7/2)-2818/12005*(1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(5/2)-5438/84035*(1-2*x)^(1/2)
*(3+5*x)^(1/2)/(2+3*x)^(3/2)+189368/588245*(1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(1/2)

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Rubi [A]
time = 0.05, antiderivative size = 222, 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 = {100, 157, 164, 114, 120} \begin {gather*} -\frac {23012 \sqrt {\frac {11}{3}} F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{588245}-\frac {189368 \sqrt {\frac {11}{3}} E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{588245}+\frac {189368 \sqrt {1-2 x} \sqrt {5 x+3}}{588245 \sqrt {3 x+2}}-\frac {5438 \sqrt {1-2 x} \sqrt {5 x+3}}{84035 (3 x+2)^{3/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {5 x+3}}{12005 (3 x+2)^{5/2}}-\frac {229 \sqrt {1-2 x} \sqrt {5 x+3}}{343 (3 x+2)^{7/2}}+\frac {11 \sqrt {5 x+3}}{7 \sqrt {1-2 x} (3 x+2)^{7/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(11*Sqrt[3 + 5*x])/(7*Sqrt[1 - 2*x]*(2 + 3*x)^(7/2)) - (229*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(343*(2 + 3*x)^(7/2))
- (2818*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(12005*(2 + 3*x)^(5/2)) - (5438*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(84035*(2 +
3*x)^(3/2)) + (189368*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(588245*Sqrt[2 + 3*x]) - (189368*Sqrt[11/3]*EllipticE[ArcS
in[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/588245 - (23012*Sqrt[11/3]*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/
33])/588245

Rule 100

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 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 {(3+5 x)^{3/2}}{(1-2 x)^{3/2} (2+3 x)^{9/2}} \, dx &=\frac {11 \sqrt {3+5 x}}{7 \sqrt {1-2 x} (2+3 x)^{7/2}}-\frac {1}{7} \int \frac {-\frac {577}{2}-490 x}{\sqrt {1-2 x} (2+3 x)^{9/2} \sqrt {3+5 x}} \, dx\\ &=\frac {11 \sqrt {3+5 x}}{7 \sqrt {1-2 x} (2+3 x)^{7/2}}-\frac {229 \sqrt {1-2 x} \sqrt {3+5 x}}{343 (2+3 x)^{7/2}}-\frac {2}{343} \int \frac {-\frac {3347}{2}-\frac {5725 x}{2}}{\sqrt {1-2 x} (2+3 x)^{7/2} \sqrt {3+5 x}} \, dx\\ &=\frac {11 \sqrt {3+5 x}}{7 \sqrt {1-2 x} (2+3 x)^{7/2}}-\frac {229 \sqrt {1-2 x} \sqrt {3+5 x}}{343 (2+3 x)^{7/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{12005 (2+3 x)^{5/2}}-\frac {4 \int \frac {-\frac {25461}{4}-\frac {21135 x}{2}}{\sqrt {1-2 x} (2+3 x)^{5/2} \sqrt {3+5 x}} \, dx}{12005}\\ &=\frac {11 \sqrt {3+5 x}}{7 \sqrt {1-2 x} (2+3 x)^{7/2}}-\frac {229 \sqrt {1-2 x} \sqrt {3+5 x}}{343 (2+3 x)^{7/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{12005 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{84035 (2+3 x)^{3/2}}-\frac {8 \int \frac {-18633-\frac {40785 x}{4}}{\sqrt {1-2 x} (2+3 x)^{3/2} \sqrt {3+5 x}} \, dx}{252105}\\ &=\frac {11 \sqrt {3+5 x}}{7 \sqrt {1-2 x} (2+3 x)^{7/2}}-\frac {229 \sqrt {1-2 x} \sqrt {3+5 x}}{343 (2+3 x)^{7/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{12005 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{84035 (2+3 x)^{3/2}}+\frac {189368 \sqrt {1-2 x} \sqrt {3+5 x}}{588245 \sqrt {2+3 x}}-\frac {16 \int \frac {-\frac {1042005}{8}-\frac {355065 x}{2}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{1764735}\\ &=\frac {11 \sqrt {3+5 x}}{7 \sqrt {1-2 x} (2+3 x)^{7/2}}-\frac {229 \sqrt {1-2 x} \sqrt {3+5 x}}{343 (2+3 x)^{7/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{12005 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{84035 (2+3 x)^{3/2}}+\frac {189368 \sqrt {1-2 x} \sqrt {3+5 x}}{588245 \sqrt {2+3 x}}+\frac {126566 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{588245}+\frac {189368 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{588245}\\ &=\frac {11 \sqrt {3+5 x}}{7 \sqrt {1-2 x} (2+3 x)^{7/2}}-\frac {229 \sqrt {1-2 x} \sqrt {3+5 x}}{343 (2+3 x)^{7/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{12005 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{84035 (2+3 x)^{3/2}}+\frac {189368 \sqrt {1-2 x} \sqrt {3+5 x}}{588245 \sqrt {2+3 x}}-\frac {189368 \sqrt {\frac {11}{3}} E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{588245}-\frac {23012 \sqrt {\frac {11}{3}} F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{588245}\\ \end {align*}

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Mathematica [A]
time = 8.00, size = 109, normalized size = 0.49 \begin {gather*} \frac {2 \left (-\frac {3 \sqrt {3+5 x} \left (-809083-2279324 x+1004571 x^2+7326810 x^3+5112936 x^4\right )}{\sqrt {1-2 x} (2+3 x)^{7/2}}+\sqrt {2} \left (94684 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )+95165 F\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )\right )\right )}{1764735} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*((-3*Sqrt[3 + 5*x]*(-809083 - 2279324*x + 1004571*x^2 + 7326810*x^3 + 5112936*x^4))/(Sqrt[1 - 2*x]*(2 + 3*x
)^(7/2)) + Sqrt[2]*(94684*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 95165*EllipticF[ArcSin[Sqrt[2/1
1]*Sqrt[3 + 5*x]], -33/2])))/1764735

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(400\) vs. \(2(162)=324\).
time = 0.11, size = 401, normalized size = 1.81

method	result	size
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \left (-\frac {88 \left (-30 x^{2}-38 x -12\right )}{16807 \sqrt {\left (-\frac {1}{2}+x \right ) \left (-30 x^{2}-38 x -12\right )}}-\frac {508 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{324135 \left (\frac {2}{3}+x \right )^{3}}+\frac {2 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{27783 \left (\frac {2}{3}+x \right )^{4}}+\frac {-\frac {397216}{117649} x^{2}-\frac {198608}{588245} x +\frac {595824}{588245}}{\sqrt {\left (\frac {2}{3}+x \right ) \left (-30 x^{2}-3 x +9\right )}}-\frac {818 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{756315 \left (\frac {2}{3}+x \right )^{2}}+\frac {138934 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{2470629 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {189368 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{2470629 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\)	\(301\)
default	\(-\frac {2 \sqrt {3+5 x}\, \sqrt {1-2 x}\, \left (5125923 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-2556468 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}[phone] \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-5112936 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}+6834564 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-3408624 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}+1518792 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-757472 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-76694040 x^{5}-155918574 x^{4}-81009855 x^{3}[phone] x^{2}[phone] x +7281747\right )}{1764735 \left (2+3 x \right )^{\frac {7}{2}} \left (10 x^{2}+x -3\right )}\)	\(401\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2/1764735*(3+5*x)^(1/2)*(1-2*x)^(1/2)*(5125923*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)-2556468*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)-5112936*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)+6834564*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)-3408624*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)+1518792*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*70^(1/2))-757472*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))-76694040*x^5-155918574*x^4-81009855*x^3+25148721*x^2+32650161*x+7281747)/(2+3*x)^(7/2)/(10*x^2+x-3)

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

[Out]

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

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Fricas [A]
time = 0.19, size = 70, normalized size = 0.32 \begin {gather*} \frac {2 \, {\left (5112936 \, x^{4} + 7326810 \, x^{3} + 1004571 \, x^{2} - 2279324 \, x - 809083\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{588245 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/588245*(5112936*x^4 + 7326810*x^3 + 1004571*x^2 - 2279324*x - 809083)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x
+ 1)/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)

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

[Out]

Exception raised: SystemError >> excessive stack use: stack is 7317 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((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^(9/2),x, algorithm="giac")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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