3.18.17 \(\int \frac {\sqrt {1-2 x}}{(2+3 x)^4 (3+5 x)^3} \, dx\)

Optimal. Leaf size=180 \[ \frac {4031135 \sqrt {1-2 x}}{1078 (5 x+3)}-\frac {182335 \sqrt {1-2 x}}{294 (5 x+3)^2}+\frac {4042 \sqrt {1-2 x}}{49 (3 x+2) (5 x+3)^2}+\frac {29 \sqrt {1-2 x}}{7 (3 x+2)^2 (5 x+3)^2}+\frac {\sqrt {1-2 x}}{3 (3 x+2)^3 (5 x+3)^2}+\frac {2528082}{49} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {551075}{11} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \]

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Rubi [A]  time = 0.07, antiderivative size = 180, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 5, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.208, Rules used = {99, 151, 156, 63, 206} \begin {gather*} \frac {4031135 \sqrt {1-2 x}}{1078 (5 x+3)}-\frac {182335 \sqrt {1-2 x}}{294 (5 x+3)^2}+\frac {4042 \sqrt {1-2 x}}{49 (3 x+2) (5 x+3)^2}+\frac {29 \sqrt {1-2 x}}{7 (3 x+2)^2 (5 x+3)^2}+\frac {\sqrt {1-2 x}}{3 (3 x+2)^3 (5 x+3)^2}+\frac {2528082}{49} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {551075}{11} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^3),x]

[Out]

(-182335*Sqrt[1 - 2*x])/(294*(3 + 5*x)^2) + Sqrt[1 - 2*x]/(3*(2 + 3*x)^3*(3 + 5*x)^2) + (29*Sqrt[1 - 2*x])/(7*
(2 + 3*x)^2*(3 + 5*x)^2) + (4042*Sqrt[1 - 2*x])/(49*(2 + 3*x)*(3 + 5*x)^2) + (4031135*Sqrt[1 - 2*x])/(1078*(3
+ 5*x)) + (2528082*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - (551075*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt
[1 - 2*x]])/11

Rule 63

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - (a*d)/b + (d*x^p)/b)^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]

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 + 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 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 156

Int[(((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)))/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :>
Dist[(b*g - a*h)/(b*c - a*d), Int[(e + f*x)^p/(a + b*x), x], x] - Dist[(d*g - c*h)/(b*c - a*d), Int[(e + f*x)
^p/(c + d*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x]

Rule 206

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

Rubi steps

\begin {align*} \int \frac {\sqrt {1-2 x}}{(2+3 x)^4 (3+5 x)^3} \, dx &=\frac {\sqrt {1-2 x}}{3 (2+3 x)^3 (3+5 x)^2}-\frac {1}{3} \int \frac {-28+45 x}{\sqrt {1-2 x} (2+3 x)^3 (3+5 x)^3} \, dx\\ &=\frac {\sqrt {1-2 x}}{3 (2+3 x)^3 (3+5 x)^2}+\frac {29 \sqrt {1-2 x}}{7 (2+3 x)^2 (3+5 x)^2}-\frac {1}{42} \int \frac {-4024+6090 x}{\sqrt {1-2 x} (2+3 x)^2 (3+5 x)^3} \, dx\\ &=\frac {\sqrt {1-2 x}}{3 (2+3 x)^3 (3+5 x)^2}+\frac {29 \sqrt {1-2 x}}{7 (2+3 x)^2 (3+5 x)^2}+\frac {4042 \sqrt {1-2 x}}{49 (2+3 x) (3+5 x)^2}-\frac {1}{294} \int \frac {-438494+606300 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)^3} \, dx\\ &=-\frac {182335 \sqrt {1-2 x}}{294 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{3 (2+3 x)^3 (3+5 x)^2}+\frac {29 \sqrt {1-2 x}}{7 (2+3 x)^2 (3+5 x)^2}+\frac {4042 \sqrt {1-2 x}}{49 (2+3 x) (3+5 x)^2}+\frac {\int \frac {-31549584+36102330 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)^2} \, dx}{6468}\\ &=-\frac {182335 \sqrt {1-2 x}}{294 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{3 (2+3 x)^3 (3+5 x)^2}+\frac {29 \sqrt {1-2 x}}{7 (2+3 x)^2 (3+5 x)^2}+\frac {4042 \sqrt {1-2 x}}{49 (2+3 x) (3+5 x)^2}+\frac {4031135 \sqrt {1-2 x}}{1078 (3+5 x)}-\frac {\int \frac {-1303277712+798164730 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)} \, dx}{71148}\\ &=-\frac {182335 \sqrt {1-2 x}}{294 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{3 (2+3 x)^3 (3+5 x)^2}+\frac {29 \sqrt {1-2 x}}{7 (2+3 x)^2 (3+5 x)^2}+\frac {4042 \sqrt {1-2 x}}{49 (2+3 x) (3+5 x)^2}+\frac {4031135 \sqrt {1-2 x}}{1078 (3+5 x)}-\frac {3792123}{49} \int \frac {1}{\sqrt {1-2 x} (2+3 x)} \, dx+\frac {2755375}{22} \int \frac {1}{\sqrt {1-2 x} (3+5 x)} \, dx\\ &=-\frac {182335 \sqrt {1-2 x}}{294 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{3 (2+3 x)^3 (3+5 x)^2}+\frac {29 \sqrt {1-2 x}}{7 (2+3 x)^2 (3+5 x)^2}+\frac {4042 \sqrt {1-2 x}}{49 (2+3 x) (3+5 x)^2}+\frac {4031135 \sqrt {1-2 x}}{1078 (3+5 x)}+\frac {3792123}{49} \operatorname {Subst}\left (\int \frac {1}{\frac {7}{2}-\frac {3 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )-\frac {2755375}{22} \operatorname {Subst}\left (\int \frac {1}{\frac {11}{2}-\frac {5 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )\\ &=-\frac {182335 \sqrt {1-2 x}}{294 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{3 (2+3 x)^3 (3+5 x)^2}+\frac {29 \sqrt {1-2 x}}{7 (2+3 x)^2 (3+5 x)^2}+\frac {4042 \sqrt {1-2 x}}{49 (2+3 x) (3+5 x)^2}+\frac {4031135 \sqrt {1-2 x}}{1078 (3+5 x)}+\frac {2528082}{49} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {551075}{11} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )\\ \end {align*}

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Mathematica [A]  time = 0.25, size = 167, normalized size = 0.93 \begin {gather*} \frac {-22497365 (1-2 x)^{3/2} (3 x+2)^3+2977568 (1-2 x)^{3/2} (3 x+2)^2+150766 (1-2 x)^{3/2} (3 x+2)+11858 (1-2 x)^{3/2}+(5 x+3) (3 x+2)^3 \left (301398449 \sqrt {1-2 x}[phone] \sqrt {21} (5 x+3) \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-378037450 \sqrt {55} (5 x+3) \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )\right )}{83006 (3 x+2)^3 (5 x+3)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^3),x]

[Out]

(11858*(1 - 2*x)^(3/2) + 150766*(1 - 2*x)^(3/2)*(2 + 3*x) + 2977568*(1 - 2*x)^(3/2)*(2 + 3*x)^2 - 22497365*(1
- 2*x)^(3/2)*(2 + 3*x)^3 + (2 + 3*x)^3*(3 + 5*x)*(301398449*Sqrt[1 - 2*x] + 611795844*Sqrt[21]*(3 + 5*x)*ArcTa
nh[Sqrt[3/7]*Sqrt[1 - 2*x]] - 378037450*Sqrt[55]*(3 + 5*x)*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]]))/(83006*(2 + 3*x
)^3*(3 + 5*x)^2)

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IntegrateAlgebraic [A]  time = 0.42, size = 141, normalized size = 0.78 \begin {gather*} \frac {-544203225 (1-2 x)^{9/2}[phone] (1-2 x)^{7/2}-17019867294 (1-2 x)^{5/2}[phone] (1-2 x)^{3/2}-14768524001 \sqrt {1-2 x}}{539 (3 (1-2 x)-7)^3 (5 (1-2 x)-11)^2}+\frac {2528082}{49} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {551075}{11} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^3),x]

[Out]

(-14768524001*Sqrt[1 - 2*x] + 25893807436*(1 - 2*x)^(3/2) - 17019867294*(1 - 2*x)^(5/2) + 4970567340*(1 - 2*x)
^(7/2) - 544203225*(1 - 2*x)^(9/2))/(539*(-7 + 3*(1 - 2*x))^3*(-11 + 5*(1 - 2*x))^2) + (2528082*Sqrt[3/7]*ArcT
anh[Sqrt[3/7]*Sqrt[1 - 2*x]])/49 - (551075*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/11

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fricas [A]  time = 1.58, size = 182, normalized size = 1.01 \begin {gather*} \frac {189018725 \, \sqrt {11} \sqrt {5} {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (\frac {\sqrt {11} \sqrt {5} \sqrt {-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right ) + 305897922 \, \sqrt {7} \sqrt {3} {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (-\frac {\sqrt {7} \sqrt {3} \sqrt {-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right ) + 77 \, {\left (544203225 \, x^{4} + 1396877220 \, x^{3} + 1343346156 \, x^{2} + 573620246 \, x + 91763734\right )} \sqrt {-2 \, x + 1}}{83006 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^3,x, algorithm="fricas")

[Out]

1/83006*(189018725*sqrt(11)*sqrt(5)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log((sqrt(11)*sqrt
(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 305897922*sqrt(7)*sqrt(3)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2
+ 564*x + 72)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(544203225*x^4 + 1396877220*x^3
+ 1343346156*x^2 + 573620246*x + 91763734)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x
+ 72)

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giac [A]  time = 1.23, size = 151, normalized size = 0.84 \begin {gather*} \frac {551075}{242} \, \sqrt {55} \log \left (\frac {{\left | -2 \, \sqrt {55} + 10 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}\right )}}\right ) - \frac {1264041}{343} \, \sqrt {21} \log \left (\frac {{\left | -2 \, \sqrt {21} + 6 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}\right )}}\right ) - \frac {125 \, {\left (1325 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - 2893 \, \sqrt {-2 \, x + 1}\right )}}{44 \, {\left (5 \, x + 3\right )}^{2}} + \frac {9 \, {\left (65673 \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - 308672 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + 362747 \, \sqrt {-2 \, x + 1}\right )}}{196 \, {\left (3 \, x + 2\right )}^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^3,x, algorithm="giac")

[Out]

551075/242*sqrt(55)*log(1/2*abs(-2*sqrt(55) + 10*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 1264041/343*
sqrt(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) - 125/44*(1325*(-2*x + 1)^
(3/2) - 2893*sqrt(-2*x + 1))/(5*x + 3)^2 + 9/196*(65673*(2*x - 1)^2*sqrt(-2*x + 1) - 308672*(-2*x + 1)^(3/2) +
362747*sqrt(-2*x + 1))/(3*x + 2)^3

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maple [A]  time = 0.02, size = 103, normalized size = 0.57 \begin {gather*} \frac {2528082 \sqrt {21}\, \arctanh \left (\frac {\sqrt {21}\, \sqrt {-2 x +1}}{7}\right )}{343}-\frac {551075 \sqrt {55}\, \arctanh \left (\frac {\sqrt {55}\, \sqrt {-2 x +1}}{11}\right )}{121}+\frac {-\frac {165625 \left (-2 x +1\right )^{\frac {3}{2}}}{11}+32875 \sqrt {-2 x +1}}{\left (-10 x -6\right )^{2}}-\frac {972 \left (\frac {7297 \left (-2 x +1\right )^{\frac {5}{2}}}{294}-\frac {22048 \left (-2 x +1\right )^{\frac {3}{2}}}{189}+\frac {7403 \sqrt {-2 x +1}}{54}\right )}{\left (-6 x -4\right )^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2*x+1)^(1/2)/(3*x+2)^4/(5*x+3)^3,x)

[Out]

62500*(-53/220*(-2*x+1)^(3/2)+263/500*(-2*x+1)^(1/2))/(-10*x-6)^2-551075/121*arctanh(1/11*55^(1/2)*(-2*x+1)^(1
/2))*55^(1/2)-972*(7297/294*(-2*x+1)^(5/2)-22048/189*(-2*x+1)^(3/2)+7403/54*(-2*x+1)^(1/2))/(-6*x-4)^3+2528082
/343*arctanh(1/7*21^(1/2)*(-2*x+1)^(1/2))*21^(1/2)

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maxima [A]  time = 1.16, size = 164, normalized size = 0.91 \begin {gather*} \frac {551075}{242} \, \sqrt {55} \log \left (-\frac {\sqrt {55} - 5 \, \sqrt {-2 \, x + 1}}{\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}}\right ) - \frac {1264041}{343} \, \sqrt {21} \log \left (-\frac {\sqrt {21} - 3 \, \sqrt {-2 \, x + 1}}{\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}}\right ) + \frac {544203225 \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - 4970567340 \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + 17019867294 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - 25893807436 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + 14768524001 \, \sqrt {-2 \, x + 1}}{539 \, {\left (675 \, {\left (2 \, x - 1\right )}^{5} + 7695 \, {\left (2 \, x - 1\right )}^{4} + 35082 \, {\left (2 \, x - 1\right )}^{3} + 79954 \, {\left (2 \, x - 1\right )}^{2} + 182182 \, x - 49588\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^3,x, algorithm="maxima")

[Out]

551075/242*sqrt(55)*log(-(sqrt(55) - 5*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 1264041/343*sqrt(21)*l
og(-(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 1/539*(544203225*(-2*x + 1)^(9/2) - 4970567
340*(-2*x + 1)^(7/2) + 17019867294*(-2*x + 1)^(5/2) - 25893807436*(-2*x + 1)^(3/2) + 14768524001*sqrt(-2*x + 1
))/(675*(2*x - 1)^5 + 7695*(2*x - 1)^4 + 35082*(2*x - 1)^3 + 79954*(2*x - 1)^2 + 182182*x - 49588)

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mupad [B]  time = 1.24, size = 125, normalized size = 0.69 \begin {gather*} \frac {2528082\,\sqrt {21}\,\mathrm {atanh}\left (\frac {\sqrt {21}\,\sqrt {1-2\,x}}{7}\right )}{343}-\frac {551075\,\sqrt {55}\,\mathrm {atanh}\left (\frac {\sqrt {55}\,\sqrt {1-2\,x}}{11}\right )}{121}+\frac {\frac {27399859\,\sqrt {1-2\,x}}{675}-\frac {3699115348\,{\left (1-2\,x\right )}^{3/2}}{51975}+\frac {1891096366\,{\left (1-2\,x\right )}^{5/2}}{40425}-\frac {110457052\,{\left (1-2\,x\right )}^{7/2}}{8085}+\frac {806227\,{\left (1-2\,x\right )}^{9/2}}{539}}{\frac {182182\,x}{675}+\frac {79954\,{\left (2\,x-1\right )}^2}{675}+\frac {3898\,{\left (2\,x-1\right )}^3}{75}+\frac {57\,{\left (2\,x-1\right )}^4}{5}+{\left (2\,x-1\right )}^5-\frac {49588}{675}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1 - 2*x)^(1/2)/((3*x + 2)^4*(5*x + 3)^3),x)

[Out]

(2528082*21^(1/2)*atanh((21^(1/2)*(1 - 2*x)^(1/2))/7))/343 - (551075*55^(1/2)*atanh((55^(1/2)*(1 - 2*x)^(1/2))
/11))/121 + ((27399859*(1 - 2*x)^(1/2))/675 - (3699115348*(1 - 2*x)^(3/2))/51975 + (1891096366*(1 - 2*x)^(5/2)
)/40425 - (110457052*(1 - 2*x)^(7/2))/8085 + (806227*(1 - 2*x)^(9/2))/539)/((182182*x)/675 + (79954*(2*x - 1)^
2)/675 + (3898*(2*x - 1)^3)/75 + (57*(2*x - 1)^4)/5 + (2*x - 1)^5 - 49588/675)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**(1/2)/(2+3*x)**4/(3+5*x)**3,x)

[Out]

Timed out

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