3.30.53 \(\int \frac {\sqrt {3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx\) [2953]

Optimal. Leaf size=220 \[ \frac {2 \sqrt {3+5 x}}{21 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {458 \sqrt {3+5 x}}{1617 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{18865 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{132055 (2+3 x)^{3/2}}+\frac {189368 \sqrt {1-2 x} \sqrt {3+5 x}}{924385 \sqrt {2+3 x}}-\frac {189368 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{84035 \sqrt {33}}-\frac {2092 \sqrt {\frac {11}{3}} F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{84035} \]

[Out]

-2092/252105*EllipticF(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-189368/2773155*EllipticE(1/7*21^(1
/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+2/21*(3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^(5/2)+458/1617*(3+5*x)^(1
/2)/(2+3*x)^(5/2)/(1-2*x)^(1/2)-2818/18865*(1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(5/2)-5438/132055*(1-2*x)^(1/2)
*(3+5*x)^(1/2)/(2+3*x)^(3/2)+189368/924385*(1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(1/2)

________________________________________________________________________________________

Rubi [A]
time = 0.06, antiderivative size = 220, 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 = {101, 157, 164, 114, 120} \begin {gather*} -\frac {2092 \sqrt {\frac {11}{3}} F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{84035}-\frac {189368 E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{84035 \sqrt {33}}+\frac {189368 \sqrt {1-2 x} \sqrt {5 x+3}}{924385 \sqrt {3 x+2}}-\frac {5438 \sqrt {1-2 x} \sqrt {5 x+3}}{132055 (3 x+2)^{3/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {5 x+3}}{18865 (3 x+2)^{5/2}}+\frac {458 \sqrt {5 x+3}}{1617 \sqrt {1-2 x} (3 x+2)^{5/2}}+\frac {2 \sqrt {5 x+3}}{21 (1-2 x)^{3/2} (3 x+2)^{5/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*Sqrt[3 + 5*x])/(21*(1 - 2*x)^(3/2)*(2 + 3*x)^(5/2)) + (458*Sqrt[3 + 5*x])/(1617*Sqrt[1 - 2*x]*(2 + 3*x)^(5/
2)) - (2818*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(18865*(2 + 3*x)^(5/2)) - (5438*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(132055*
(2 + 3*x)^(3/2)) + (189368*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/(924385*Sqrt[2 + 3*x]) - (189368*EllipticE[ArcSin[Sqrt
[3/7]*Sqrt[1 - 2*x]], 35/33])/(84035*Sqrt[33]) - (2092*Sqrt[11/3]*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 3
5/33])/84035

Rule 101

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(a + b*
x)^(m + 1)*(c + d*x)^n*((e + f*x)^(p + 1)/((m + 1)*(b*e - a*f))), x] - Dist[1/((m + 1)*(b*e - a*f)), Int[(a +
b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f*x)^p*Simp[d*e*n + c*f*(m + p + 2) + d*f*(m + n + p + 2)*x, x], x], x] /;
FreeQ[{a, b, c, d, e, f, p}, x] && LtQ[m, -1] && GtQ[n, 0] && (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 {\sqrt {3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx &=\frac {2 \sqrt {3+5 x}}{21 (1-2 x)^{3/2} (2+3 x)^{5/2}}-\frac {2}{21} \int \frac {-31-\frac {105 x}{2}}{(1-2 x)^{3/2} (2+3 x)^{7/2} \sqrt {3+5 x}} \, dx\\ &=\frac {2 \sqrt {3+5 x}}{21 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {458 \sqrt {3+5 x}}{1617 \sqrt {1-2 x} (2+3 x)^{5/2}}+\frac {4 \int \frac {\frac {10041}{4}+\frac {17175 x}{4}}{\sqrt {1-2 x} (2+3 x)^{7/2} \sqrt {3+5 x}} \, dx}{1617}\\ &=\frac {2 \sqrt {3+5 x}}{21 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {458 \sqrt {3+5 x}}{1617 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{18865 (2+3 x)^{5/2}}+\frac {8 \int \frac {\frac {76383}{8}+\frac {63405 x}{4}}{\sqrt {1-2 x} (2+3 x)^{5/2} \sqrt {3+5 x}} \, dx}{56595}\\ &=\frac {2 \sqrt {3+5 x}}{21 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {458 \sqrt {3+5 x}}{1617 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{18865 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{132055 (2+3 x)^{3/2}}+\frac {16 \int \frac {\frac {55899}{2}+\frac {122355 x}{8}}{\sqrt {1-2 x} (2+3 x)^{3/2} \sqrt {3+5 x}} \, dx}{1188495}\\ &=\frac {2 \sqrt {3+5 x}}{21 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {458 \sqrt {3+5 x}}{1617 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{18865 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{132055 (2+3 x)^{3/2}}+\frac {189368 \sqrt {1-2 x} \sqrt {3+5 x}}{924385 \sqrt {2+3 x}}+\frac {32 \int \frac {\frac {3126015}{16}+\frac {1065195 x}{4}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{8319465}\\ &=\frac {2 \sqrt {3+5 x}}{21 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {458 \sqrt {3+5 x}}{1617 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{18865 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{132055 (2+3 x)^{3/2}}+\frac {189368 \sqrt {1-2 x} \sqrt {3+5 x}}{924385 \sqrt {2+3 x}}+\frac {11506 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{84035}+\frac {189368 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{924385}\\ &=\frac {2 \sqrt {3+5 x}}{21 (1-2 x)^{3/2} (2+3 x)^{5/2}}+\frac {458 \sqrt {3+5 x}}{1617 \sqrt {1-2 x} (2+3 x)^{5/2}}-\frac {2818 \sqrt {1-2 x} \sqrt {3+5 x}}{18865 (2+3 x)^{5/2}}-\frac {5438 \sqrt {1-2 x} \sqrt {3+5 x}}{132055 (2+3 x)^{3/2}}+\frac {189368 \sqrt {1-2 x} \sqrt {3+5 x}}{924385 \sqrt {2+3 x}}-\frac {189368 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{84035 \sqrt {33}}-\frac {2092 \sqrt {\frac {11}{3}} F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{84035}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 8.09, size = 108, normalized size = 0.49 \begin {gather*} \frac {2 \left (\frac {\sqrt {3+5 x} \left (1339677-807691 x-7133292 x^2+2723436 x^3+10225872 x^4\right )}{(1-2 x)^{3/2} (2+3 x)^{5/2}}+\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 )}{2773155} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(2*((Sqrt[3 + 5*x]*(1339677 - 807691*x - 7133292*x^2 + 2723436*x^3 + 10225872*x^4))/((1 - 2*x)^(3/2)*(2 + 3*x)
^(5/2)) + Sqrt[2]*(94684*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] + 95165*EllipticF[ArcSin[Sqrt[2/11
]*Sqrt[3 + 5*x]], -33/2])))/2773155

________________________________________________________________________________________

Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(397\) vs. \(2(162)=324\).
time = 0.11, size = 398, normalized size = 1.81

method	result	size
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \left (\frac {4 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{7203 \left (-\frac {1}{2}+x \right )^{2}}-\frac {2624 \left (-30 x^{2}-38 x -12\right )}{554631 \sqrt {\left (-\frac {1}{2}+x \right ) \left (-30 x^{2}-38 x -12\right )}}-\frac {2 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{5145 \left (\frac {2}{3}+x \right )^{3}}+\frac {-\frac {36816}{16807} x^{2}-\frac {18408}{84035} x +\frac {55224}{84035}}{\sqrt {\left (\frac {2}{3}+x \right ) \left (-30 x^{2}-3 x +9\right )}}+\frac {2 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{5145 \left (\frac {2}{3}+x \right )^{2}}+\frac {138934 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{3882417 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {189368 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{3882417 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\)	\(301\)
default	\(-\frac {2 \sqrt {1-2 x}\, \left (3417282 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-1704312 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}+2847735 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-1420260 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-759396 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}+378736 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-759396 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )+378736 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-51129360 x^{5}-44294796 x^{4}[phone] x^{3}[phone] x^{2}-4275312 x -4019031\right )}{2773155 \left (2+3 x \right )^{\frac {5}{2}} \left (-1+2 x \right )^{2} \sqrt {3+5 x}}\)	\(398\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2/2773155*(1-2*x)^(1/2)*(3417282*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)-1704312*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)+2847735*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)-1420260*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)-759396*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)+378736*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
)-759396*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))+378736
*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))-51129360*x^5-4
4294796*x^4+27496152*x^3+25438331*x^2-4275312*x-4019031)/(2+3*x)^(5/2)/(-1+2*x)^2/(3+5*x)^(1/2)

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Fricas [A]
time = 0.35, size = 70, normalized size = 0.32 \begin {gather*} \frac {2 \, {\left (10225872 \, x^{4} + 2723436 \, x^{3} - 7133292 \, x^{2} - 807691 \, x + 1339677\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2773155 \, {\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((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^(7/2),x, algorithm="fricas")

[Out]

2/2773155*(10225872*x^4 + 2723436*x^3 - 7133292*x^2 - 807691*x + 1339677)*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)

________________________________________________________________________________________

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

[Out]

Exception raised: SystemError >> excessive stack use: stack is 4847 deep

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {\sqrt {5\,x+3}}{{\left (1-2\,x\right )}^{5/2}\,{\left (3\,x+2\right )}^{7/2}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________