3.30.62 \(\int \frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx\) [2962]

Optimal. Leaf size=253 \[ -\frac {1313411}{630} \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}-\frac {1310203 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{4620}-\frac {6277}{154} \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}-\frac {225}{22} \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}-\frac {203 (2+3 x)^{5/2} (3+5 x)^{5/2}}{33 \sqrt {1-2 x}}+\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}-\frac {174654791 \sqrt {\frac {11}{3}} E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{12600}-\frac {1313411 \sqrt {\frac {11}{3}} F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3150} \]

[Out]

1/3*(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)-174654791/37800*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(
1/2))*33^(1/2)-1313411/9450*EllipticF(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-203/33*(2+3*x)^(5/2
)*(3+5*x)^(5/2)/(1-2*x)^(1/2)-225/22*(2+3*x)^(3/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2)-1310203/4620*(3+5*x)^(3/2)*(1-2
*x)^(1/2)*(2+3*x)^(1/2)-6277/154*(3+5*x)^(5/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2)-1313411/630*(1-2*x)^(1/2)*(2+3*x)^(
1/2)*(3+5*x)^(1/2)

________________________________________________________________________________________

Rubi [A]
time = 0.07, antiderivative size = 253, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 6, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {99, 155, 159, 164, 114, 120} \begin {gather*} -\frac {1313411 \sqrt {\frac {11}{3}} F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3150}-\frac {174654791 \sqrt {\frac {11}{3}} E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{12600}+\frac {(5 x+3)^{5/2} (3 x+2)^{7/2}}{3 (1-2 x)^{3/2}}-\frac {203 (5 x+3)^{5/2} (3 x+2)^{5/2}}{33 \sqrt {1-2 x}}-\frac {225}{22} \sqrt {1-2 x} (5 x+3)^{5/2} (3 x+2)^{3/2}-\frac {6277}{154} \sqrt {1-2 x} (5 x+3)^{5/2} \sqrt {3 x+2}-\frac {1310203 \sqrt {1-2 x} (5 x+3)^{3/2} \sqrt {3 x+2}}{4620}-\frac {1313411}{630} \sqrt {1-2 x} \sqrt {5 x+3} \sqrt {3 x+2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-1313411*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x])/630 - (1310203*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2
))/4620 - (6277*Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*(3 + 5*x)^(5/2))/154 - (225*Sqrt[1 - 2*x]*(2 + 3*x)^(3/2)*(3 + 5*x
)^(5/2))/22 - (203*(2 + 3*x)^(5/2)*(3 + 5*x)^(5/2))/(33*Sqrt[1 - 2*x]) + ((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2))/(3*
(1 - 2*x)^(3/2)) - (174654791*Sqrt[11/3]*EllipticE[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/12600 - (1313411*S
qrt[11/3]*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/3150

Rule 99

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/(b*(m + 1))), x] - Dist[1/(b*(m + 1)), Int[(a + b*x)^(m + 1)*(c + d*x)^(n
- 1)*(e + f*x)^(p - 1)*Simp[d*e*n + c*f*p + d*f*(n + p)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f}, x] && LtQ[m
, -1] && GtQ[n, 0] && GtQ[p, 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 155

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*((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 - 1)*(e + f*x)^p*Simp[b*c*(f*g - e*h)*(m + 1) + (
b*g - a*h)*(d*e*n + c*f*(p + 1)) + d*(b*(f*g - e*h)*(m + 1) + f*(b*g - a*h)*(n + p + 1))*x, x], x], x] /; Free
Q[{a, b, c, d, e, f, g, h, p}, x] && LtQ[m, -1] && GtQ[n, 0] && IntegersQ[2*m, 2*n, 2*p]

Rule 159

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[h*(a + b*x)^m*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(d*f*(m + n + p + 2))), x] + Dist[1/(d*f*(m + n
+ p + 2)), Int[(a + b*x)^(m - 1)*(c + d*x)^n*(e + f*x)^p*Simp[a*d*f*g*(m + n + p + 2) - h*(b*c*e*m + a*(d*e*(
n + 1) + c*f*(p + 1))) + (b*d*f*g*(m + n + p + 2) + h*(a*d*f*m - b*(d*e*(m + n + 1) + c*f*(m + p + 1))))*x, x]
, x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && GtQ[m, 0] && NeQ[m + n + p + 2, 0] && 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 {(2+3 x)^{7/2} (3+5 x)^{5/2}}{(1-2 x)^{5/2}} \, dx &=\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}-\frac {1}{3} \int \frac {(2+3 x)^{5/2} (3+5 x)^{3/2} \left (\frac {113}{2}+90 x\right )}{(1-2 x)^{3/2}} \, dx\\ &=-\frac {203 (2+3 x)^{5/2} (3+5 x)^{5/2}}{33 \sqrt {1-2 x}}+\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}-\frac {1}{33} \int \frac {\left (-\frac {19235}{2}-\frac {30375 x}{2}\right ) (2+3 x)^{3/2} (3+5 x)^{3/2}}{\sqrt {1-2 x}} \, dx\\ &=-\frac {225}{22} \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}-\frac {203 (2+3 x)^{5/2} (3+5 x)^{5/2}}{33 \sqrt {1-2 x}}+\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}+\frac {\int \frac {\sqrt {2+3 x} (3+5 x)^{3/2} \left (\frac {5436675}{4}+\frac {4236975 x}{2}\right )}{\sqrt {1-2 x}} \, dx}{1485}\\ &=-\frac {6277}{154} \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}-\frac {225}{22} \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}-\frac {203 (2+3 x)^{5/2} (3+5 x)^{5/2}}{33 \sqrt {1-2 x}}+\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}-\frac {\int \frac {\left (-\frac {579705075}{4}-\frac {884387025 x}{4}\right ) (3+5 x)^{3/2}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{51975}\\ &=-\frac {1310203 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{4620}-\frac {6277}{154} \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}-\frac {225}{22} \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}-\frac {203 (2+3 x)^{5/2} (3+5 x)^{5/2}}{33 \sqrt {1-2 x}}+\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}+\frac {\int \frac {\sqrt {3+5 x} \left (\frac {76051906425}{8}+\frac {29256230025 x}{2}\right )}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{779625}\\ &=-\frac {1313411}{630} \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}-\frac {1310203 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{4620}-\frac {6277}{154} \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}-\frac {225}{22} \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}-\frac {203 (2+3 x)^{5/2} (3+5 x)^{5/2}}{33 \sqrt {1-2 x}}+\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}-\frac {\int \frac {-\frac {2462988693825}{8}-\frac {3890435469525 x}{8}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{7016625}\\ &=-\frac {1313411}{630} \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}-\frac {1310203 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{4620}-\frac {6277}{154} \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}-\frac {225}{22} \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}-\frac {203 (2+3 x)^{5/2} (3+5 x)^{5/2}}{33 \sqrt {1-2 x}}+\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}+\frac {14447521 \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{6300}+\frac {174654791 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{12600}\\ &=-\frac {1313411}{630} \sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}-\frac {1310203 \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}}{4620}-\frac {6277}{154} \sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}-\frac {225}{22} \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}-\frac {203 (2+3 x)^{5/2} (3+5 x)^{5/2}}{33 \sqrt {1-2 x}}+\frac {(2+3 x)^{7/2} (3+5 x)^{5/2}}{3 (1-2 x)^{3/2}}-\frac {174654791 \sqrt {\frac {11}{3}} E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{12600}-\frac {1313411 \sqrt {\frac {11}{3}} F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{3150}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 9.49, size = 135, normalized size = 0.53 \begin {gather*} -\frac {30 \sqrt {2+3 x} \sqrt {3+5 x} \left (4641769-12151171 x+2783146 x^2+1279350 x^3+486900 x^4+94500 x^5\right )[phone] \sqrt {2-4 x} (-1+2 x) E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )-87969665 \sqrt {2-4 x} (-1+2 x) F\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )}{37800 (1-2 x)^{3/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/37800*(30*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]*(4641769 - 12151171*x + 2783146*x^2 + 1279350*x^3 + 486900*x^4 + 9450
0*x^5) + 174654791*Sqrt[2 - 4*x]*(-1 + 2*x)*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 87969665*Sqrt
[2 - 4*x]*(-1 + 2*x)*EllipticF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])/(1 - 2*x)^(3/2)

________________________________________________________________________________________

Maple [A]
time = 0.10, size = 249, normalized size = 0.98

method	result	size
default	\(\frac {\left (-42525000 x^{7}[phone] \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-173370252 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-272970000 x^{6}-174654791 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )[phone] \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-870250500 x^{5}-2069287200 x^{4}[phone] x^{3}[phone] x^{2}-458597550 x -835518420\right ) \sqrt {1-2 x}\, \sqrt {3+5 x}\, \sqrt {2+3 x}}{37800 \left (30 x^{3}+23 x^{2}-7 x -6\right ) \left (-1+2 x \right )}\)	\(249\)
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \sqrt {3+5 x}\, \sqrt {2+3 x}\, \left (\frac {41503 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{384 \left (-\frac {1}{2}+x \right )^{2}}+\frac {-\frac {1549625}{32} x^{2}-\frac {5888575}{96} x -\frac {309925}{16}}{\sqrt {\left (-\frac {1}{2}+x \right ) \left (-30 x^{2}-38 x -12\right )}}-\frac {75 x^{3} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{4}-\frac {1615 x^{2} \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{14}-\frac {40825 x \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{112}-\frac {4474921 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{5040}+\frac {110571883 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{52920 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {174654791 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{52920 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \left (15 x^{2}+19 x +6\right )}\)	\(320\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/37800*(-42525000*x^7+349309582*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)-173370252*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)-272970000*x^6-174654791*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))[phone]*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))-870250500*x^5-2069287200*x^4+3651350730*x^3+4336405140*x^2-458597550*x-835518420)*(1-2*x)^
(1/2)*(3+5*x)^(1/2)*(2+3*x)^(1/2)/(30*x^3+23*x^2-7*x-6)/(-1+2*x)

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Fricas [A]
time = 0.17, size = 60, normalized size = 0.24 \begin {gather*} -\frac {{\left (94500 \, x^{5} + 486900 \, x^{4} + 1279350 \, x^{3} + 2783146 \, x^{2} - 12151171 \, x + 4641769\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{1260 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/1260*(94500*x^5 + 486900*x^4 + 1279350*x^3 + 2783146*x^2 - 12151171*x + 4641769)*sqrt(5*x + 3)*sqrt(3*x + 2
)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)

________________________________________________________________________________________

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

[Out]

Exception raised: SystemError >> excessive stack use: stack is 8856 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((2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm="giac")

[Out]

integrate((5*x + 3)^(5/2)*(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 {{\left (3\,x+2\right )}^{7/2}\,{\left (5\,x+3\right )}^{5/2}}{{\left (1-2\,x\right )}^{5/2}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________