3.2560 \(\int \frac {1}{(1-2 x)^{3/2} (2+3 x)^5 \sqrt {3+5 x}} \, dx\)

Optimal. Leaf size=173 \[ -\frac {7986105 \sqrt {5 x+3}}{845152 \sqrt {1-2 x}}+\frac {698295 \sqrt {5 x+3}}{21952 \sqrt {1-2 x} (3 x+2)}+\frac {6621 \sqrt {5 x+3}}{1568 \sqrt {1-2 x} (3 x+2)^2}+\frac {263 \sqrt {5 x+3}}{392 \sqrt {1-2 x} (3 x+2)^3}+\frac {3 \sqrt {5 x+3}}{28 \sqrt {1-2 x} (3 x+2)^4}-\frac {24922335 \tan ^{-1}\left (\frac {\sqrt {1-2 x}}{\sqrt {7} \sqrt {5 x+3}}\right )}{153664 \sqrt {7}} \]

[Out]

-24922335/1075648*arctan(1/7*(1-2*x)^(1/2)*7^(1/2)/(3+5*x)^(1/2))*7^(1/2)-7986105/845152*(3+5*x)^(1/2)/(1-2*x)
^(1/2)+3/28*(3+5*x)^(1/2)/(2+3*x)^4/(1-2*x)^(1/2)+263/392*(3+5*x)^(1/2)/(2+3*x)^3/(1-2*x)^(1/2)+6621/1568*(3+5
*x)^(1/2)/(2+3*x)^2/(1-2*x)^(1/2)+698295/21952*(3+5*x)^(1/2)/(2+3*x)/(1-2*x)^(1/2)

________________________________________________________________________________________

Rubi [A]  time = 0.06, antiderivative size = 173, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 6, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {103, 151, 152, 12, 93, 204} \[ -\frac {7986105 \sqrt {5 x+3}}{845152 \sqrt {1-2 x}}+\frac {698295 \sqrt {5 x+3}}{21952 \sqrt {1-2 x} (3 x+2)}+\frac {6621 \sqrt {5 x+3}}{1568 \sqrt {1-2 x} (3 x+2)^2}+\frac {263 \sqrt {5 x+3}}{392 \sqrt {1-2 x} (3 x+2)^3}+\frac {3 \sqrt {5 x+3}}{28 \sqrt {1-2 x} (3 x+2)^4}-\frac {24922335 \tan ^{-1}\left (\frac {\sqrt {1-2 x}}{\sqrt {7} \sqrt {5 x+3}}\right )}{153664 \sqrt {7}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-7986105*Sqrt[3 + 5*x])/(845152*Sqrt[1 - 2*x]) + (3*Sqrt[3 + 5*x])/(28*Sqrt[1 - 2*x]*(2 + 3*x)^4) + (263*Sqrt
[3 + 5*x])/(392*Sqrt[1 - 2*x]*(2 + 3*x)^3) + (6621*Sqrt[3 + 5*x])/(1568*Sqrt[1 - 2*x]*(2 + 3*x)^2) + (698295*S
qrt[3 + 5*x])/(21952*Sqrt[1 - 2*x]*(2 + 3*x)) - (24922335*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(1536
64*Sqrt[7])

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 93

Int[(((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_))/((e_.) + (f_.)*(x_)), x_Symbol] :> With[{q = Denomin
ator[m]}, Dist[q, Subst[Int[x^(q*(m + 1) - 1)/(b*e - a*f - (d*e - c*f)*x^q), x], x, (a + b*x)^(1/q)/(c + d*x)^
(1/q)], x]] /; FreeQ[{a, b, c, d, e, f}, x] && EqQ[m + n + 1, 0] && RationalQ[n] && LtQ[-1, m, 0] && SimplerQ[
a + b*x, c + d*x]

Rule 103

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] &&
IntegerQ[m] && (IntegerQ[n] || IntegersQ[2*n, 2*p])

Rule 151

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] && IntegerQ[m]

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 204

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /
; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])

Rubi steps

\begin {align*} \int \frac {1}{(1-2 x)^{3/2} (2+3 x)^5 \sqrt {3+5 x}} \, dx &=\frac {3 \sqrt {3+5 x}}{28 \sqrt {1-2 x} (2+3 x)^4}+\frac {1}{28} \int \frac {\frac {103}{2}-120 x}{(1-2 x)^{3/2} (2+3 x)^4 \sqrt {3+5 x}} \, dx\\ &=\frac {3 \sqrt {3+5 x}}{28 \sqrt {1-2 x} (2+3 x)^4}+\frac {263 \sqrt {3+5 x}}{392 \sqrt {1-2 x} (2+3 x)^3}+\frac {1}{588} \int \frac {\frac {14787}{4}-11835 x}{(1-2 x)^{3/2} (2+3 x)^3 \sqrt {3+5 x}} \, dx\\ &=\frac {3 \sqrt {3+5 x}}{28 \sqrt {1-2 x} (2+3 x)^4}+\frac {263 \sqrt {3+5 x}}{392 \sqrt {1-2 x} (2+3 x)^3}+\frac {6621 \sqrt {3+5 x}}{1568 \sqrt {1-2 x} (2+3 x)^2}+\frac {\int \frac {\frac {1180305}{8}-695205 x}{(1-2 x)^{3/2} (2+3 x)^2 \sqrt {3+5 x}} \, dx}{8232}\\ &=\frac {3 \sqrt {3+5 x}}{28 \sqrt {1-2 x} (2+3 x)^4}+\frac {263 \sqrt {3+5 x}}{392 \sqrt {1-2 x} (2+3 x)^3}+\frac {6621 \sqrt {3+5 x}}{1568 \sqrt {1-2 x} (2+3 x)^2}+\frac {698295 \sqrt {3+5 x}}{21952 \sqrt {1-2 x} (2+3 x)}+\frac {\int \frac {-\frac {21066255}{16}-\frac {73320975 x}{4}}{(1-2 x)^{3/2} (2+3 x) \sqrt {3+5 x}} \, dx}{57624}\\ &=-\frac {7986105 \sqrt {3+5 x}}{845152 \sqrt {1-2 x}}+\frac {3 \sqrt {3+5 x}}{28 \sqrt {1-2 x} (2+3 x)^4}+\frac {263 \sqrt {3+5 x}}{392 \sqrt {1-2 x} (2+3 x)^3}+\frac {6621 \sqrt {3+5 x}}{1568 \sqrt {1-2 x} (2+3 x)^2}+\frac {698295 \sqrt {3+5 x}}{21952 \sqrt {1-2 x} (2+3 x)}-\frac {\int -\frac {5757059385}{32 \sqrt {1-2 x} (2+3 x) \sqrt {3+5 x}} \, dx}{2218524}\\ &=-\frac {7986105 \sqrt {3+5 x}}{845152 \sqrt {1-2 x}}+\frac {3 \sqrt {3+5 x}}{28 \sqrt {1-2 x} (2+3 x)^4}+\frac {263 \sqrt {3+5 x}}{392 \sqrt {1-2 x} (2+3 x)^3}+\frac {6621 \sqrt {3+5 x}}{1568 \sqrt {1-2 x} (2+3 x)^2}+\frac {698295 \sqrt {3+5 x}}{21952 \sqrt {1-2 x} (2+3 x)}+\frac {24922335 \int \frac {1}{\sqrt {1-2 x} (2+3 x) \sqrt {3+5 x}} \, dx}{307328}\\ &=-\frac {7986105 \sqrt {3+5 x}}{845152 \sqrt {1-2 x}}+\frac {3 \sqrt {3+5 x}}{28 \sqrt {1-2 x} (2+3 x)^4}+\frac {263 \sqrt {3+5 x}}{392 \sqrt {1-2 x} (2+3 x)^3}+\frac {6621 \sqrt {3+5 x}}{1568 \sqrt {1-2 x} (2+3 x)^2}+\frac {698295 \sqrt {3+5 x}}{21952 \sqrt {1-2 x} (2+3 x)}+\frac {24922335 \operatorname {Subst}\left (\int \frac {1}{-7-x^2} \, dx,x,\frac {\sqrt {1-2 x}}{\sqrt {3+5 x}}\right )}{153664}\\ &=-\frac {7986105 \sqrt {3+5 x}}{845152 \sqrt {1-2 x}}+\frac {3 \sqrt {3+5 x}}{28 \sqrt {1-2 x} (2+3 x)^4}+\frac {263 \sqrt {3+5 x}}{392 \sqrt {1-2 x} (2+3 x)^3}+\frac {6621 \sqrt {3+5 x}}{1568 \sqrt {1-2 x} (2+3 x)^2}+\frac {698295 \sqrt {3+5 x}}{21952 \sqrt {1-2 x} (2+3 x)}-\frac {24922335 \tan ^{-1}\left (\frac {\sqrt {1-2 x}}{\sqrt {7} \sqrt {3+5 x}}\right )}{153664 \sqrt {7}}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.08, size = 95, normalized size = 0.55 \[ \frac {-7 \sqrt {5 x+3} \left (1293749010 x^4+1998242055 x^3+482249808 x^2-491393004 x-205593328\right )-274145685 \sqrt {7-14 x} (3 x+2)^4 \tan ^{-1}\left (\frac {\sqrt {1-2 x}}{\sqrt {7} \sqrt {5 x+3}}\right )}{11832128 \sqrt {1-2 x} (3 x+2)^4} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-7*Sqrt[3 + 5*x]*(-205593328 - 491393004*x + 482249808*x^2 + 1998242055*x^3 + 1293749010*x^4) - 274145685*Sqr
t[7 - 14*x]*(2 + 3*x)^4*ArcTan[Sqrt[1 - 2*x]/(Sqrt[7]*Sqrt[3 + 5*x])])/(11832128*Sqrt[1 - 2*x]*(2 + 3*x)^4)

________________________________________________________________________________________

fricas [A]  time = 0.88, size = 131, normalized size = 0.76 \[ -\frac {274145685 \, \sqrt {7} {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \arctan \left (\frac {\sqrt {7} {\left (37 \, x + 20\right )} \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1}}{14 \, {\left (10 \, x^{2} + x - 3\right )}}\right ) - 14 \, {\left (1293749010 \, x^{4} + 1998242055 \, x^{3} + 482249808 \, x^{2} - 491393004 \, x - 205593328\right )} \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1}}{23664256 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/23664256*(274145685*sqrt(7)*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*arctan(1/14*sqrt(7)*(37*x +
20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1293749010*x^4 + 1998242055*x^3 + 482249808*x^2 - 491
393004*x - 205593328)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)

________________________________________________________________________________________

giac [B]  time = 4.03, size = 394, normalized size = 2.28 \[ \frac {4984467}{4302592} \, \sqrt {70} \sqrt {10} {\left (\pi + 2 \, \arctan \left (-\frac {\sqrt {70} \sqrt {5 \, x + 3} {\left (\frac {{\left (\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \, {\left (\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}\right )}}\right )\right )} - \frac {64 \, \sqrt {5} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5}}{924385 \, {\left (2 \, x - 1\right )}} + \frac {99 \, \sqrt {10} {\left (4411181 \, {\left (\frac {\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}{\sqrt {5 \, x + 3}} - \frac {4 \, \sqrt {5 \, x + 3}}{\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}\right )}^{7} + 2388710520 \, {\left (\frac {\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}{\sqrt {5 \, x + 3}} - \frac {4 \, \sqrt {5 \, x + 3}}{\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}\right )}^{5} + 506212728000 \, {\left (\frac {\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}{\sqrt {5 \, x + 3}} - \frac {4 \, \sqrt {5 \, x + 3}}{\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}\right )}^{3} + \frac {38676680000000 \, {\left (\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}\right )}}{\sqrt {5 \, x + 3}} - \frac {154706720000000 \, \sqrt {5 \, x + 3}}{\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}\right )}}{537824 \, {\left ({\left (\frac {\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}{\sqrt {5 \, x + 3}} - \frac {4 \, \sqrt {5 \, x + 3}}{\sqrt {2} \sqrt {-10 \, x + 5} - \sqrt {22}}\right )}^{2} + 280\right )}^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4984467/4302592*sqrt(70)*sqrt(10)*(pi + 2*arctan(-1/140*sqrt(70)*sqrt(5*x + 3)*((sqrt(2)*sqrt(-10*x + 5) - sqr
t(22))^2/(5*x + 3) - 4)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))) - 64/924385*sqrt(5)*sqrt(5*x + 3)*sqrt(-10*x +
5)/(2*x - 1) + 99/537824*sqrt(10)*(4411181*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x +
3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^7 + 2388710520*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) -
4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^5 + 506212728000*((sqrt(2)*sqrt(-10*x + 5) - sqrt(22))/s
qrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^3 + 38676680000000*(sqrt(2)*sqrt(-10*x +
5) - sqrt(22))/sqrt(5*x + 3) - 154706720000000*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))/(((sqrt(2)*
sqrt(-10*x + 5) - sqrt(22))/sqrt(5*x + 3) - 4*sqrt(5*x + 3)/(sqrt(2)*sqrt(-10*x + 5) - sqrt(22)))^2 + 280)^4

________________________________________________________________________________________

maple [B]  time = 0.02, size = 305, normalized size = 1.76 \[ \frac {\left (44411600970 \sqrt {7}\, x^{5} \arctan \left (\frac {\left (37 x +20\right ) \sqrt {7}}{14 \sqrt {-10 x^{2}-x +3}}\right )[phone] \sqrt {7}\, x^{4} \arctan \left (\frac {\left (37 x +20\right ) \sqrt {7}}{14 \sqrt {-10 x^{2}-x +3}}\right )[phone] \sqrt {-10 x^{2}-x +3}\, x^{4}[phone] \sqrt {7}\, x^{3} \arctan \left (\frac {\left (37 x +20\right ) \sqrt {7}}{14 \sqrt {-10 x^{2}-x +3}}\right )[phone] \sqrt {-10 x^{2}-x +3}\, x^{3}-6579496440 \sqrt {7}\, x^{2} \arctan \left (\frac {\left (37 x +20\right ) \sqrt {7}}{14 \sqrt {-10 x^{2}-x +3}}\right )[phone] \sqrt {-10 x^{2}-x +3}\, x^{2}-17545323840 \sqrt {7}\, x \arctan \left (\frac {\left (37 x +20\right ) \sqrt {7}}{14 \sqrt {-10 x^{2}-x +3}}\right )-6879502056 \sqrt {-10 x^{2}-x +3}\, x -4386330960 \sqrt {7}\, \arctan \left (\frac {\left (37 x +20\right ) \sqrt {7}}{14 \sqrt {-10 x^{2}-x +3}}\right )-2878306592 \sqrt {-10 x^{2}-x +3}\right ) \sqrt {5 x +3}\, \sqrt {-2 x +1}}{23664256 \left (3 x +2\right )^{4} \left (2 x -1\right ) \sqrt {-10 x^{2}-x +3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/23664256*(44411600970*7^(1/2)*x^5*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))[phone]*7^(1/2)*x^4
*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x+3)^(1/2))[phone]*7^(1/2)*x^3*arctan(1/14*(37*x+20)*7^(1/2)/(-10
*x^2-x+3)^(1/2))[phone]*(-10*x^2-x+3)^(1/2)*x^4-6579496440*7^(1/2)*x^2*arctan(1/14*(37*x+20)*7^(1/2)/(-10
*x^2-x+3)^(1/2))[phone]*(-10*x^2-x+3)^(1/2)*x^3-17545323840*7^(1/2)*x*arctan(1/14*(37*x+20)*7^(1/2)/(-10*
x^2-x+3)^(1/2))[phone]*(-10*x^2-x+3)^(1/2)*x^2-4386330960*7^(1/2)*arctan(1/14*(37*x+20)*7^(1/2)/(-10*x^2-x
+3)^(1/2))-6879502056*(-10*x^2-x+3)^(1/2)*x-2878306592*(-10*x^2-x+3)^(1/2))*(5*x+3)^(1/2)*(-2*x+1)^(1/2)/(3*x+
2)^4/(2*x-1)/(-10*x^2-x+3)^(1/2)

________________________________________________________________________________________

maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {5 \, x + 3} {\left (3 \, x + 2\right )}^{5} {\left (-2 \, x + 1\right )}^{\frac {3}{2}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {1}{{\left (1-2\,x\right )}^{3/2}\,{\left (3\,x+2\right )}^5\,\sqrt {5\,x+3}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

________________________________________________________________________________________