3.2380 \(\int \frac {1}{(a+b \sqrt [3]{x})^3 x^4} \, dx\)

Optimal. Leaf size=183 \[ \frac {165 b^9 \log \left (a+b \sqrt [3]{x}\right )}{a^{12}}-\frac {55 b^9 \log (x)}{a^{12}}-\frac {30 b^9}{a^{11} \left (a+b \sqrt [3]{x}\right )}-\frac {135 b^8}{a^{11} \sqrt [3]{x}}-\frac {3 b^9}{2 a^{10} \left (a+b \sqrt [3]{x}\right )^2}+\frac {54 b^7}{a^{10} x^{2/3}}-\frac {28 b^6}{a^9 x}+\frac {63 b^5}{4 a^8 x^{4/3}}-\frac {9 b^4}{a^7 x^{5/3}}+\frac {5 b^3}{a^6 x^2}-\frac {18 b^2}{7 a^5 x^{7/3}}+\frac {9 b}{8 a^4 x^{8/3}}-\frac {1}{3 a^3 x^3} \]

[Out]

-3/2*b^9/a^10/(a+b*x^(1/3))^2-30*b^9/a^11/(a+b*x^(1/3))-1/3/a^3/x^3+9/8*b/a^4/x^(8/3)-18/7*b^2/a^5/x^(7/3)+5*b
^3/a^6/x^2-9*b^4/a^7/x^(5/3)+63/4*b^5/a^8/x^(4/3)-28*b^6/a^9/x+54*b^7/a^10/x^(2/3)-135*b^8/a^11/x^(1/3)+165*b^
9*ln(a+b*x^(1/3))/a^12-55*b^9*ln(x)/a^12

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Rubi [A]  time = 0.14, antiderivative size = 183, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {266, 44} \[ \frac {54 b^7}{a^{10} x^{2/3}}+\frac {63 b^5}{4 a^8 x^{4/3}}-\frac {9 b^4}{a^7 x^{5/3}}+\frac {5 b^3}{a^6 x^2}-\frac {18 b^2}{7 a^5 x^{7/3}}-\frac {30 b^9}{a^{11} \left (a+b \sqrt [3]{x}\right )}-\frac {3 b^9}{2 a^{10} \left (a+b \sqrt [3]{x}\right )^2}-\frac {135 b^8}{a^{11} \sqrt [3]{x}}-\frac {28 b^6}{a^9 x}+\frac {165 b^9 \log \left (a+b \sqrt [3]{x}\right )}{a^{12}}-\frac {55 b^9 \log (x)}{a^{12}}+\frac {9 b}{8 a^4 x^{8/3}}-\frac {1}{3 a^3 x^3} \]

Antiderivative was successfully verified.

[In]

Int[1/((a + b*x^(1/3))^3*x^4),x]

[Out]

(-3*b^9)/(2*a^10*(a + b*x^(1/3))^2) - (30*b^9)/(a^11*(a + b*x^(1/3))) - 1/(3*a^3*x^3) + (9*b)/(8*a^4*x^(8/3))
- (18*b^2)/(7*a^5*x^(7/3)) + (5*b^3)/(a^6*x^2) - (9*b^4)/(a^7*x^(5/3)) + (63*b^5)/(4*a^8*x^(4/3)) - (28*b^6)/(
a^9*x) + (54*b^7)/(a^10*x^(2/3)) - (135*b^8)/(a^11*x^(1/3)) + (165*b^9*Log[a + b*x^(1/3)])/a^12 - (55*b^9*Log[
x])/a^12

Rule 44

Int[((a_) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*
x)^n, x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0] && ILtQ[m, 0] && IntegerQ[n] &&  !(IGtQ[n, 0] && L
tQ[m + n + 2, 0])

Rule 266

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Dist[1/n, Subst[Int[x^(Simplify[(m + 1)/n] - 1)*(a
+ b*x)^p, x], x, x^n], x] /; FreeQ[{a, b, m, n, p}, x] && IntegerQ[Simplify[(m + 1)/n]]

Rubi steps

\begin {align*} \int \frac {1}{\left (a+b \sqrt [3]{x}\right )^3 x^4} \, dx &=3 \operatorname {Subst}\left (\int \frac {1}{x^{10} (a+b x)^3} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {1}{a^3 x^{10}}-\frac {3 b}{a^4 x^9}+\frac {6 b^2}{a^5 x^8}-\frac {10 b^3}{a^6 x^7}+\frac {15 b^4}{a^7 x^6}-\frac {21 b^5}{a^8 x^5}+\frac {28 b^6}{a^9 x^4}-\frac {36 b^7}{a^{10} x^3}+\frac {45 b^8}{a^{11} x^2}-\frac {55 b^9}{a^{12} x}+\frac {b^{10}}{a^{10} (a+b x)^3}+\frac {10 b^{10}}{a^{11} (a+b x)^2}+\frac {55 b^{10}}{a^{12} (a+b x)}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {3 b^9}{2 a^{10} \left (a+b \sqrt [3]{x}\right )^2}-\frac {30 b^9}{a^{11} \left (a+b \sqrt [3]{x}\right )}-\frac {1}{3 a^3 x^3}+\frac {9 b}{8 a^4 x^{8/3}}-\frac {18 b^2}{7 a^5 x^{7/3}}+\frac {5 b^3}{a^6 x^2}-\frac {9 b^4}{a^7 x^{5/3}}+\frac {63 b^5}{4 a^8 x^{4/3}}-\frac {28 b^6}{a^9 x}+\frac {54 b^7}{a^{10} x^{2/3}}-\frac {135 b^8}{a^{11} \sqrt [3]{x}}+\frac {165 b^9 \log \left (a+b \sqrt [3]{x}\right )}{a^{12}}-\frac {55 b^9 \log (x)}{a^{12}}\\ \end {align*}

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Mathematica [A]  time = 0.28, size = 167, normalized size = 0.91 \[ -\frac {\frac {a \left (56 a^{10}-77 a^9 b \sqrt [3]{x}+110 a^8 b^2 x^{2/3}-165 a^7 b^3 x+264 a^6 b^4 x^{4/3}-462 a^5 b^5 x^{5/3}+924 a^4 b^6 x^2-2310 a^3 b^7 x^{7/3}+9240 a^2 b^8 x^{8/3}+41580 a b^9 x^3+27720 b^{10} x^{10/3}\right )}{x^3 \left (a+b \sqrt [3]{x}\right )^2}-27720 b^9 \log \left (a+b \sqrt [3]{x}\right )+9240 b^9 \log (x)}{168 a^{12}} \]

Antiderivative was successfully verified.

[In]

Integrate[1/((a + b*x^(1/3))^3*x^4),x]

[Out]

-1/168*((a*(56*a^10 - 77*a^9*b*x^(1/3) + 110*a^8*b^2*x^(2/3) - 165*a^7*b^3*x + 264*a^6*b^4*x^(4/3) - 462*a^5*b
^5*x^(5/3) + 924*a^4*b^6*x^2 - 2310*a^3*b^7*x^(7/3) + 9240*a^2*b^8*x^(8/3) + 41580*a*b^9*x^3 + 27720*b^10*x^(1
0/3)))/((a + b*x^(1/3))^2*x^3) - 27720*b^9*Log[a + b*x^(1/3)] + 9240*b^9*Log[x])/a^12

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fricas [A]  time = 0.67, size = 263, normalized size = 1.44 \[ -\frac {9240 \, a^{3} b^{12} x^{4} + 13860 \, a^{6} b^{9} x^{3} + 3080 \, a^{9} b^{6} x^{2} - 728 \, a^{12} b^{3} x + 56 \, a^{15} - 27720 \, {\left (b^{15} x^{5} + 2 \, a^{3} b^{12} x^{4} + a^{6} b^{9} x^{3}\right )} \log \left (b x^{\frac {1}{3}} + a\right ) + 27720 \, {\left (b^{15} x^{5} + 2 \, a^{3} b^{12} x^{4} + a^{6} b^{9} x^{3}\right )} \log \left (x^{\frac {1}{3}}\right ) + 18 \, {\left (1540 \, a b^{14} x^{4} + 2695 \, a^{4} b^{11} x^{3} + 990 \, a^{7} b^{8} x^{2} - 99 \, a^{10} b^{5} x + 24 \, a^{13} b^{2}\right )} x^{\frac {2}{3}} - 63 \, {\left (220 \, a^{2} b^{13} x^{4} + 352 \, a^{5} b^{10} x^{3} + 99 \, a^{8} b^{7} x^{2} - 18 \, a^{11} b^{4} x + 3 \, a^{14} b\right )} x^{\frac {1}{3}}}{168 \, {\left (a^{12} b^{6} x^{5} + 2 \, a^{15} b^{3} x^{4} + a^{18} x^{3}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*x^(1/3))^3/x^4,x, algorithm="fricas")

[Out]

-1/168*(9240*a^3*b^12*x^4 + 13860*a^6*b^9*x^3 + 3080*a^9*b^6*x^2 - 728*a^12*b^3*x + 56*a^15 - 27720*(b^15*x^5
+ 2*a^3*b^12*x^4 + a^6*b^9*x^3)*log(b*x^(1/3) + a) + 27720*(b^15*x^5 + 2*a^3*b^12*x^4 + a^6*b^9*x^3)*log(x^(1/
3)) + 18*(1540*a*b^14*x^4 + 2695*a^4*b^11*x^3 + 990*a^7*b^8*x^2 - 99*a^10*b^5*x + 24*a^13*b^2)*x^(2/3) - 63*(2
20*a^2*b^13*x^4 + 352*a^5*b^10*x^3 + 99*a^8*b^7*x^2 - 18*a^11*b^4*x + 3*a^14*b)*x^(1/3))/(a^12*b^6*x^5 + 2*a^1
5*b^3*x^4 + a^18*x^3)

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giac [A]  time = 0.17, size = 156, normalized size = 0.85 \[ \frac {165 \, b^{9} \log \left ({\left | b x^{\frac {1}{3}} + a \right |}\right )}{a^{12}} - \frac {55 \, b^{9} \log \left ({\left | x \right |}\right )}{a^{12}} - \frac {27720 \, a b^{10} x^{\frac {10}{3}} + 41580 \, a^{2} b^{9} x^{3} + 9240 \, a^{3} b^{8} x^{\frac {8}{3}} - 2310 \, a^{4} b^{7} x^{\frac {7}{3}} + 924 \, a^{5} b^{6} x^{2} - 462 \, a^{6} b^{5} x^{\frac {5}{3}} + 264 \, a^{7} b^{4} x^{\frac {4}{3}} - 165 \, a^{8} b^{3} x + 110 \, a^{9} b^{2} x^{\frac {2}{3}} - 77 \, a^{10} b x^{\frac {1}{3}} + 56 \, a^{11}}{168 \, {\left (b x^{\frac {1}{3}} + a\right )}^{2} a^{12} x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*x^(1/3))^3/x^4,x, algorithm="giac")

[Out]

165*b^9*log(abs(b*x^(1/3) + a))/a^12 - 55*b^9*log(abs(x))/a^12 - 1/168*(27720*a*b^10*x^(10/3) + 41580*a^2*b^9*
x^3 + 9240*a^3*b^8*x^(8/3) - 2310*a^4*b^7*x^(7/3) + 924*a^5*b^6*x^2 - 462*a^6*b^5*x^(5/3) + 264*a^7*b^4*x^(4/3
) - 165*a^8*b^3*x + 110*a^9*b^2*x^(2/3) - 77*a^10*b*x^(1/3) + 56*a^11)/((b*x^(1/3) + a)^2*a^12*x^3)

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maple [A]  time = 0.02, size = 156, normalized size = 0.85 \[ -\frac {3 b^{9}}{2 \left (b \,x^{\frac {1}{3}}+a \right )^{2} a^{10}}-\frac {30 b^{9}}{\left (b \,x^{\frac {1}{3}}+a \right ) a^{11}}-\frac {55 b^{9} \ln \relax (x )}{a^{12}}+\frac {165 b^{9} \ln \left (b \,x^{\frac {1}{3}}+a \right )}{a^{12}}-\frac {135 b^{8}}{a^{11} x^{\frac {1}{3}}}+\frac {54 b^{7}}{a^{10} x^{\frac {2}{3}}}-\frac {28 b^{6}}{a^{9} x}+\frac {63 b^{5}}{4 a^{8} x^{\frac {4}{3}}}-\frac {9 b^{4}}{a^{7} x^{\frac {5}{3}}}+\frac {5 b^{3}}{a^{6} x^{2}}-\frac {18 b^{2}}{7 a^{5} x^{\frac {7}{3}}}+\frac {9 b}{8 a^{4} x^{\frac {8}{3}}}-\frac {1}{3 a^{3} x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(b*x^(1/3)+a)^3/x^4,x)

[Out]

-3/2*b^9/a^10/(b*x^(1/3)+a)^2-30*b^9/a^11/(b*x^(1/3)+a)-1/3/a^3/x^3+9/8*b/a^4/x^(8/3)-18/7*b^2/a^5/x^(7/3)+5*b
^3/a^6/x^2-9*b^4/a^7/x^(5/3)+63/4*b^5/a^8/x^(4/3)-28*b^6/a^9/x+54*b^7/a^10/x^(2/3)-135*b^8/a^11/x^(1/3)+165*b^
9*ln(b*x^(1/3)+a)/a^12-55*b^9*ln(x)/a^12

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maxima [A]  time = 0.56, size = 165, normalized size = 0.90 \[ -\frac {27720 \, b^{10} x^{\frac {10}{3}} + 41580 \, a b^{9} x^{3} + 9240 \, a^{2} b^{8} x^{\frac {8}{3}} - 2310 \, a^{3} b^{7} x^{\frac {7}{3}} + 924 \, a^{4} b^{6} x^{2} - 462 \, a^{5} b^{5} x^{\frac {5}{3}} + 264 \, a^{6} b^{4} x^{\frac {4}{3}} - 165 \, a^{7} b^{3} x + 110 \, a^{8} b^{2} x^{\frac {2}{3}} - 77 \, a^{9} b x^{\frac {1}{3}} + 56 \, a^{10}}{168 \, {\left (a^{11} b^{2} x^{\frac {11}{3}} + 2 \, a^{12} b x^{\frac {10}{3}} + a^{13} x^{3}\right )}} + \frac {165 \, b^{9} \log \left (b x^{\frac {1}{3}} + a\right )}{a^{12}} - \frac {55 \, b^{9} \log \relax (x)}{a^{12}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*x^(1/3))^3/x^4,x, algorithm="maxima")

[Out]

-1/168*(27720*b^10*x^(10/3) + 41580*a*b^9*x^3 + 9240*a^2*b^8*x^(8/3) - 2310*a^3*b^7*x^(7/3) + 924*a^4*b^6*x^2
- 462*a^5*b^5*x^(5/3) + 264*a^6*b^4*x^(4/3) - 165*a^7*b^3*x + 110*a^8*b^2*x^(2/3) - 77*a^9*b*x^(1/3) + 56*a^10
)/(a^11*b^2*x^(11/3) + 2*a^12*b*x^(10/3) + a^13*x^3) + 165*b^9*log(b*x^(1/3) + a)/a^12 - 55*b^9*log(x)/a^12

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mupad [B]  time = 1.29, size = 159, normalized size = 0.87 \[ \frac {330\,b^9\,\mathrm {atanh}\left (\frac {2\,b\,x^{1/3}}{a}+1\right )}{a^{12}}-\frac {\frac {1}{3\,a}-\frac {11\,b\,x^{1/3}}{24\,a^2}-\frac {55\,b^3\,x}{56\,a^4}+\frac {55\,b^2\,x^{2/3}}{84\,a^3}+\frac {11\,b^6\,x^2}{2\,a^7}+\frac {11\,b^4\,x^{4/3}}{7\,a^5}-\frac {11\,b^5\,x^{5/3}}{4\,a^6}+\frac {495\,b^9\,x^3}{2\,a^{10}}-\frac {55\,b^7\,x^{7/3}}{4\,a^8}+\frac {55\,b^8\,x^{8/3}}{a^9}+\frac {165\,b^{10}\,x^{10/3}}{a^{11}}}{a^2\,x^3+b^2\,x^{11/3}+2\,a\,b\,x^{10/3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^4*(a + b*x^(1/3))^3),x)

[Out]

(330*b^9*atanh((2*b*x^(1/3))/a + 1))/a^12 - (1/(3*a) - (11*b*x^(1/3))/(24*a^2) - (55*b^3*x)/(56*a^4) + (55*b^2
*x^(2/3))/(84*a^3) + (11*b^6*x^2)/(2*a^7) + (11*b^4*x^(4/3))/(7*a^5) - (11*b^5*x^(5/3))/(4*a^6) + (495*b^9*x^3
)/(2*a^10) - (55*b^7*x^(7/3))/(4*a^8) + (55*b^8*x^(8/3))/a^9 + (165*b^10*x^(10/3))/a^11)/(a^2*x^3 + b^2*x^(11/
3) + 2*a*b*x^(10/3))

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sympy [A]  time = 22.57, size = 847, normalized size = 4.63 \[ \begin {cases} \frac {\tilde {\infty }}{x^{4}} & \text {for}\: a = 0 \wedge b = 0 \\- \frac {1}{3 a^{3} x^{3}} & \text {for}\: b = 0 \\- \frac {1}{4 b^{3} x^{4}} & \text {for}\: a = 0 \\- \frac {56 a^{11} x^{\frac {2}{3}}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} + \frac {77 a^{10} b x}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {110 a^{9} b^{2} x^{\frac {4}{3}}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} + \frac {165 a^{8} b^{3} x^{\frac {5}{3}}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {264 a^{7} b^{4} x^{2}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} + \frac {462 a^{6} b^{5} x^{\frac {7}{3}}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {924 a^{5} b^{6} x^{\frac {8}{3}}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} + \frac {2310 a^{4} b^{7} x^{3}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {9240 a^{3} b^{8} x^{\frac {10}{3}}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {9240 a^{2} b^{9} x^{\frac {11}{3}} \log {\relax (x )}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} + \frac {27720 a^{2} b^{9} x^{\frac {11}{3}} \log {\left (\frac {a}{b} + \sqrt [3]{x} \right )}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {41580 a^{2} b^{9} x^{\frac {11}{3}}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {18480 a b^{10} x^{4} \log {\relax (x )}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} + \frac {55440 a b^{10} x^{4} \log {\left (\frac {a}{b} + \sqrt [3]{x} \right )}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {27720 a b^{10} x^{4}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} - \frac {9240 b^{11} x^{\frac {13}{3}} \log {\relax (x )}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} + \frac {27720 b^{11} x^{\frac {13}{3}} \log {\left (\frac {a}{b} + \sqrt [3]{x} \right )}}{168 a^{14} x^{\frac {11}{3}} + 336 a^{13} b x^{4} + 168 a^{12} b^{2} x^{\frac {13}{3}}} & \text {otherwise} \end {cases} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*x**(1/3))**3/x**4,x)

[Out]

Piecewise((zoo/x**4, Eq(a, 0) & Eq(b, 0)), (-1/(3*a**3*x**3), Eq(b, 0)), (-1/(4*b**3*x**4), Eq(a, 0)), (-56*a*
*11*x**(2/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 77*a**10*b*x/(168*a**14*x**
(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 110*a**9*b**2*x**(4/3)/(168*a**14*x**(11/3) + 336*a**1
3*b*x**4 + 168*a**12*b**2*x**(13/3)) + 165*a**8*b**3*x**(5/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a*
*12*b**2*x**(13/3)) - 264*a**7*b**4*x**2/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) +
462*a**6*b**5*x**(7/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 924*a**5*b**6*x*
*(8/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 2310*a**4*b**7*x**3/(168*a**14*x*
*(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 9240*a**3*b**8*x**(10/3)/(168*a**14*x**(11/3) + 336*a
**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 9240*a**2*b**9*x**(11/3)*log(x)/(168*a**14*x**(11/3) + 336*a**13*b*x
**4 + 168*a**12*b**2*x**(13/3)) + 27720*a**2*b**9*x**(11/3)*log(a/b + x**(1/3))/(168*a**14*x**(11/3) + 336*a**
13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 41580*a**2*b**9*x**(11/3)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 16
8*a**12*b**2*x**(13/3)) - 18480*a*b**10*x**4*log(x)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x
**(13/3)) + 55440*a*b**10*x**4*log(a/b + x**(1/3))/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x*
*(13/3)) - 27720*a*b**10*x**4/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) - 9240*b**11
*x**(13/3)*log(x)/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)) + 27720*b**11*x**(13/3)*
log(a/b + x**(1/3))/(168*a**14*x**(11/3) + 336*a**13*b*x**4 + 168*a**12*b**2*x**(13/3)), True))

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