Integrand size = 24, antiderivative size = 114 \[ \int \frac {(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {484}{7203 (1-2 x)^{3/2}}+\frac {2728}{16807 \sqrt {1-2 x}}-\frac {\sqrt {1-2 x}}{1029 (2+3 x)^3}+\frac {193 \sqrt {1-2 x}}{14406 (2+3 x)^2}-\frac {1721 \sqrt {1-2 x}}{33614 (2+3 x)}-\frac {1415 \text {arctanh}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )}{2401 \sqrt {21}} \] Output:
484/7203/(1-2*x)^(3/2)+2728/16807/(1-2*x)^(1/2)-1/1029*(1-2*x)^(1/2)/(2+3* x)^3+193/14406*(1-2*x)^(1/2)/(2+3*x)^2-1721*(1-2*x)^(1/2)/(67228+100842*x) -1415/50421*21^(1/2)*arctanh(1/7*21^(1/2)*(1-2*x)^(1/2))
Time = 0.20 (sec) , antiderivative size = 70, normalized size of antiderivative = 0.61 \[ \int \frac {(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {-\frac {7 \left (-23872-83655 x-26319 x^2+169800 x^3+152820 x^4\right )}{2 (1-2 x)^{3/2} (2+3 x)^3}-1415 \sqrt {21} \text {arctanh}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )}{50421} \] Input:
Integrate[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]
Output:
((-7*(-23872 - 83655*x - 26319*x^2 + 169800*x^3 + 152820*x^4))/(2*(1 - 2*x )^(3/2)*(2 + 3*x)^3) - 1415*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/504 21
Time = 0.26 (sec) , antiderivative size = 143, normalized size of antiderivative = 1.25, number of steps used = 9, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {100, 27, 87, 52, 52, 61, 73, 219}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \frac {(5 x+3)^2}{(1-2 x)^{5/2} (3 x+2)^4} \, dx\) |
\(\Big \downarrow \) 100 |
\(\displaystyle \frac {121}{42 (1-2 x)^{3/2} (3 x+2)^3}-\frac {1}{42} \int -\frac {3 (247-175 x)}{(1-2 x)^{3/2} (3 x+2)^4}dx\) |
\(\Big \downarrow \) 27 |
\(\displaystyle \frac {1}{14} \int \frac {247-175 x}{(1-2 x)^{3/2} (3 x+2)^4}dx+\frac {121}{42 (1-2 x)^{3/2} (3 x+2)^3}\) |
\(\Big \downarrow \) 87 |
\(\displaystyle \frac {1}{14} \left (\frac {566}{9} \int \frac {1}{(1-2 x)^{3/2} (3 x+2)^3}dx-\frac {1091}{63 \sqrt {1-2 x} (3 x+2)^3}\right )+\frac {121}{42 (1-2 x)^{3/2} (3 x+2)^3}\) |
\(\Big \downarrow \) 52 |
\(\displaystyle \frac {1}{14} \left (\frac {566}{9} \left (\frac {5}{14} \int \frac {1}{(1-2 x)^{3/2} (3 x+2)^2}dx-\frac {1}{14 \sqrt {1-2 x} (3 x+2)^2}\right )-\frac {1091}{63 \sqrt {1-2 x} (3 x+2)^3}\right )+\frac {121}{42 (1-2 x)^{3/2} (3 x+2)^3}\) |
\(\Big \downarrow \) 52 |
\(\displaystyle \frac {1}{14} \left (\frac {566}{9} \left (\frac {5}{14} \left (\frac {3}{7} \int \frac {1}{(1-2 x)^{3/2} (3 x+2)}dx-\frac {1}{7 \sqrt {1-2 x} (3 x+2)}\right )-\frac {1}{14 \sqrt {1-2 x} (3 x+2)^2}\right )-\frac {1091}{63 \sqrt {1-2 x} (3 x+2)^3}\right )+\frac {121}{42 (1-2 x)^{3/2} (3 x+2)^3}\) |
\(\Big \downarrow \) 61 |
\(\displaystyle \frac {1}{14} \left (\frac {566}{9} \left (\frac {5}{14} \left (\frac {3}{7} \left (\frac {3}{7} \int \frac {1}{\sqrt {1-2 x} (3 x+2)}dx+\frac {2}{7 \sqrt {1-2 x}}\right )-\frac {1}{7 \sqrt {1-2 x} (3 x+2)}\right )-\frac {1}{14 \sqrt {1-2 x} (3 x+2)^2}\right )-\frac {1091}{63 \sqrt {1-2 x} (3 x+2)^3}\right )+\frac {121}{42 (1-2 x)^{3/2} (3 x+2)^3}\) |
\(\Big \downarrow \) 73 |
\(\displaystyle \frac {1}{14} \left (\frac {566}{9} \left (\frac {5}{14} \left (\frac {3}{7} \left (\frac {2}{7 \sqrt {1-2 x}}-\frac {3}{7} \int \frac {1}{\frac {7}{2}-\frac {3}{2} (1-2 x)}d\sqrt {1-2 x}\right )-\frac {1}{7 \sqrt {1-2 x} (3 x+2)}\right )-\frac {1}{14 \sqrt {1-2 x} (3 x+2)^2}\right )-\frac {1091}{63 \sqrt {1-2 x} (3 x+2)^3}\right )+\frac {121}{42 (1-2 x)^{3/2} (3 x+2)^3}\) |
\(\Big \downarrow \) 219 |
\(\displaystyle \frac {1}{14} \left (\frac {566}{9} \left (\frac {5}{14} \left (\frac {3}{7} \left (\frac {2}{7 \sqrt {1-2 x}}-\frac {2}{7} \sqrt {\frac {3}{7}} \text {arctanh}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )\right )-\frac {1}{7 \sqrt {1-2 x} (3 x+2)}\right )-\frac {1}{14 \sqrt {1-2 x} (3 x+2)^2}\right )-\frac {1091}{63 \sqrt {1-2 x} (3 x+2)^3}\right )+\frac {121}{42 (1-2 x)^{3/2} (3 x+2)^3}\) |
Input:
Int[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]
Output:
121/(42*(1 - 2*x)^(3/2)*(2 + 3*x)^3) + (-1091/(63*Sqrt[1 - 2*x]*(2 + 3*x)^ 3) + (566*(-1/14*1/(Sqrt[1 - 2*x]*(2 + 3*x)^2) + (5*(-1/7*1/(Sqrt[1 - 2*x] *(2 + 3*x)) + (3*(2/(7*Sqrt[1 - 2*x]) - (2*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqr t[1 - 2*x]])/7))/7))/14))/9)/14
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[ (a + b*x)^(m + 1)*((c + d*x)^(n + 1)/((b*c - a*d)*(m + 1))), x] - Simp[d*(( m + n + 2)/((b*c - a*d)*(m + 1))) Int[(a + b*x)^(m + 1)*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && ILtQ[m, -1] && FractionQ[n] && LtQ[n, 0]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[ (a + b*x)^(m + 1)*((c + d*x)^(n + 1)/((b*c - a*d)*(m + 1))), x] - Simp[d*(( m + n + 2)/((b*c - a*d)*(m + 1))) Int[(a + b*x)^(m + 1)*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && LtQ[m, -1] && !(LtQ[n, -1] && (EqQ[a, 0 ] || (NeQ[c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && IntLinearQ[a, b, c, d , m, n, x]
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[ {p = Denominator[m]}, Simp[p/b Subst[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] && Lt Q[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntL inearQ[a, b, c, d, m, n, x]
Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p _.), x_] :> Simp[(-(b*e - a*f))*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(f*(p + 1)*(c*f - d*e))), x] - Simp[(a*d*f*(n + p + 2) - b*(d*e*(n + 1) + c*f*(p + 1)))/(f*(p + 1)*(c*f - d*e)) Int[(c + d*x)^n*(e + f*x)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && LtQ[p, -1] && ( !LtQ[n, -1] || Intege rQ[p] || !(IntegerQ[n] || !(EqQ[e, 0] || !(EqQ[c, 0] || LtQ[p, n]))))
Int[((a_.) + (b_.)*(x_))^2*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^( p_), x_] :> Simp[(b*c - a*d)^2*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(d^2*(d *e - c*f)*(n + 1))), x] - Simp[1/(d^2*(d*e - c*f)*(n + 1)) Int[(c + d*x)^ (n + 1)*(e + f*x)^p*Simp[a^2*d^2*f*(n + p + 2) + b^2*c*(d*e*(n + 1) + c*f*( p + 1)) - 2*a*b*d*(d*e*(n + 1) + c*f*(p + 1)) - b^2*d*(d*e - c*f)*(n + 1)*x , x], x], x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && (LtQ[n, -1] || (EqQ[n + p + 3, 0] && NeQ[n, -1] && (SumSimplerQ[n, 1] || !SumSimplerQ[p, 1])))
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1/(Rt[a, 2]*Rt[-b, 2]))* ArcTanh[Rt[-b, 2]*(x/Rt[a, 2])], x] /; FreeQ[{a, b}, x] && NegQ[a/b] && (Gt Q[a, 0] || LtQ[b, 0])
Time = 0.24 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.55
method | result | size |
risch | \(\frac {152820 x^{4}+169800 x^{3}-26319 x^{2}-83655 x -23872}{14406 \left (2+3 x \right )^{3} \sqrt {1-2 x}\, \left (-1+2 x \right )}-\frac {1415 \sqrt {21}\, \operatorname {arctanh}\left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right )}{50421}\) | \(63\) |
pseudoelliptic | \(\frac {\frac {11936}{7203}-\frac {1415 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {21}\, \left (2+3 x \right )^{3} \operatorname {arctanh}\left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right )}{50421}-\frac {25470 x^{4}}{2401}-\frac {28300 x^{3}}{2401}+\frac {8773 x^{2}}{4802}+\frac {27885 x}{4802}}{\left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{3}}\) | \(69\) |
derivativedivides | \(\frac {484}{7203 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {2728}{16807 \sqrt {1-2 x}}+\frac {\frac {15489 \left (1-2 x \right )^{\frac {5}{2}}}{16807}-\frac {1420 \left (1-2 x \right )^{\frac {3}{2}}}{343}+\frac {1595 \sqrt {1-2 x}}{343}}{\left (-4-6 x \right )^{3}}-\frac {1415 \sqrt {21}\, \operatorname {arctanh}\left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right )}{50421}\) | \(75\) |
default | \(\frac {484}{7203 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {2728}{16807 \sqrt {1-2 x}}+\frac {\frac {15489 \left (1-2 x \right )^{\frac {5}{2}}}{16807}-\frac {1420 \left (1-2 x \right )^{\frac {3}{2}}}{343}+\frac {1595 \sqrt {1-2 x}}{343}}{\left (-4-6 x \right )^{3}}-\frac {1415 \sqrt {21}\, \operatorname {arctanh}\left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right )}{50421}\) | \(75\) |
trager | \(-\frac {\left (152820 x^{4}+169800 x^{3}-26319 x^{2}-83655 x -23872\right ) \sqrt {1-2 x}}{14406 \left (2+3 x \right )^{3} \left (-1+2 x \right )^{2}}-\frac {1415 \operatorname {RootOf}\left (\textit {\_Z}^{2}-21\right ) \ln \left (-\frac {3 \operatorname {RootOf}\left (\textit {\_Z}^{2}-21\right ) x -5 \operatorname {RootOf}\left (\textit {\_Z}^{2}-21\right )-21 \sqrt {1-2 x}}{2+3 x}\right )}{100842}\) | \(90\) |
Input:
int((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^4,x,method=_RETURNVERBOSE)
Output:
1/14406*(152820*x^4+169800*x^3-26319*x^2-83655*x-23872)/(2+3*x)^3/(1-2*x)^ (1/2)/(-1+2*x)-1415/50421*21^(1/2)*arctanh(1/7*21^(1/2)*(1-2*x)^(1/2))
Time = 0.10 (sec) , antiderivative size = 114, normalized size of antiderivative = 1.00 \[ \int \frac {(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {1415 \, \sqrt {21} {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (\frac {3 \, x + \sqrt {21} \sqrt {-2 \, x + 1} - 5}{3 \, x + 2}\right ) - 7 \, {\left (152820 \, x^{4} + 169800 \, x^{3} - 26319 \, x^{2} - 83655 \, x - 23872\right )} \sqrt {-2 \, x + 1}}{100842 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \] Input:
integrate((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm="fricas")
Output:
1/100842*(1415*sqrt(21)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*lo g((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 7*(152820*x^4 + 169800* x^3 - 26319*x^2 - 83655*x - 23872)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45 *x^3 - 58*x^2 + 4*x + 8)
Timed out. \[ \int \frac {(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\text {Timed out} \] Input:
integrate((3+5*x)**2/(1-2*x)**(5/2)/(2+3*x)**4,x)
Output:
Timed out
Time = 0.11 (sec) , antiderivative size = 110, normalized size of antiderivative = 0.96 \[ \int \frac {(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {1415}{100842} \, \sqrt {21} \log \left (-\frac {\sqrt {21} - 3 \, \sqrt {-2 \, x + 1}}{\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}}\right ) + \frac {38205 \, {\left (2 \, x - 1\right )}^{4} + 237720 \, {\left (2 \, x - 1\right )}^{3} + 457611 \, {\left (2 \, x - 1\right )}^{2} + 375144 \, x - 353584}{7203 \, {\left (27 \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - 189 \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + 441 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - 343 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}\right )}} \] Input:
integrate((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm="maxima")
Output:
1415/100842*sqrt(21)*log(-(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt (-2*x + 1))) + 1/7203*(38205*(2*x - 1)^4 + 237720*(2*x - 1)^3 + 457611*(2* x - 1)^2 + 375144*x - 353584)/(27*(-2*x + 1)^(9/2) - 189*(-2*x + 1)^(7/2) + 441*(-2*x + 1)^(5/2) - 343*(-2*x + 1)^(3/2))
Time = 0.13 (sec) , antiderivative size = 95, normalized size of antiderivative = 0.83 \[ \int \frac {(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {1415}{100842} \, \sqrt {21} \log \left (\frac {{\left | -2 \, \sqrt {21} + 6 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}\right )}}\right ) + \frac {38205 \, {\left (2 \, x - 1\right )}^{4} + 237720 \, {\left (2 \, x - 1\right )}^{3} + 457611 \, {\left (2 \, x - 1\right )}^{2} + 375144 \, x - 353584}{7203 \, {\left (3 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - 7 \, \sqrt {-2 \, x + 1}\right )}^{3}} \] Input:
integrate((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm="giac")
Output:
1415/100842*sqrt(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 1/7203*(38205*(2*x - 1)^4 + 237720*(2*x - 1)^3 + 4 57611*(2*x - 1)^2 + 375144*x - 353584)/(3*(-2*x + 1)^(3/2) - 7*sqrt(-2*x + 1))^3
Time = 1.12 (sec) , antiderivative size = 92, normalized size of antiderivative = 0.81 \[ \int \frac {(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=-\frac {\frac {2552\,x}{1323}+\frac {3113\,{\left (2\,x-1\right )}^2}{1323}+\frac {11320\,{\left (2\,x-1\right )}^3}{9261}+\frac {1415\,{\left (2\,x-1\right )}^4}{7203}-\frac {7216}{3969}}{\frac {343\,{\left (1-2\,x\right )}^{3/2}}{27}-\frac {49\,{\left (1-2\,x\right )}^{5/2}}{3}+7\,{\left (1-2\,x\right )}^{7/2}-{\left (1-2\,x\right )}^{9/2}}-\frac {1415\,\sqrt {21}\,\mathrm {atanh}\left (\frac {\sqrt {21}\,\sqrt {1-2\,x}}{7}\right )}{50421} \] Input:
int((5*x + 3)^2/((1 - 2*x)^(5/2)*(3*x + 2)^4),x)
Output:
- ((2552*x)/1323 + (3113*(2*x - 1)^2)/1323 + (11320*(2*x - 1)^3)/9261 + (1 415*(2*x - 1)^4)/7203 - 7216/3969)/((343*(1 - 2*x)^(3/2))/27 - (49*(1 - 2* x)^(5/2))/3 + 7*(1 - 2*x)^(7/2) - (1 - 2*x)^(9/2)) - (1415*21^(1/2)*atanh( (21^(1/2)*(1 - 2*x)^(1/2))/7))/50421
Time = 0.15 (sec) , antiderivative size = 302, normalized size of antiderivative = 2.65 \[ \int \frac {(3+5 x)^2}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {76410 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right ) x^{4}+114615 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right ) x^{3}+25470 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right ) x^{2}-28300 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right ) x -11320 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right )-76410 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right ) x^{4}-114615 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right ) x^{3}-25470 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right ) x^{2}+28300 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right ) x +11320 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right )+1069740 x^{4}+1188600 x^{3}-184233 x^{2}-585585 x -167104}{100842 \sqrt {-2 x +1}\, \left (54 x^{4}+81 x^{3}+18 x^{2}-20 x -8\right )} \] Input:
int((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^4,x)
Output:
(76410*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21))*x**4 + 114615*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21))*x**3 + 25470*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21))*x**2 - 28300*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21))*x - 1 1320*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21)) - 76410* sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21))*x**4 - 114615 *sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21))*x**3 - 25470 *sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21))*x**2 + 28300 *sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21))*x + 11320*sq rt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21)) + 1069740*x**4 + 1188600*x**3 - 184233*x**2 - 585585*x - 167104)/(100842*sqrt( - 2*x + 1) *(54*x**4 + 81*x**3 + 18*x**2 - 20*x - 8))