3.760 \(\int \frac{1}{x^9 (a+b x^3)^{4/3} (c+d x^3)} \, dx\)
Optimal. Leaf size=351 \[ -\frac{\left (a+b x^3\right )^{2/3} \left (-12 a^2 b c d^2-20 a^3 d^3-9 a b^2 c^2 d+81 b^3 c^3\right )}{40 a^4 c^3 x^2 (b c-a d)}+\frac{\left (a+b x^3\right )^{2/3} (9 b c-4 a d) (a d+3 b c)}{20 a^3 c^2 x^5 (b c-a d)}-\frac{\left (a+b x^3\right )^{2/3} (9 b c-a d)}{8 a^2 c x^8 (b c-a d)}+\frac{d^4 \log \left (c+d x^3\right )}{6 c^{11/3} (b c-a d)^{4/3}}-\frac{d^4 \log \left (\frac{x \sqrt [3]{b c-a d}}{\sqrt [3]{c}}-\sqrt [3]{a+b x^3}\right )}{2 c^{11/3} (b c-a d)^{4/3}}+\frac{d^4 \tan ^{-1}\left (\frac{\frac{2 x \sqrt [3]{b c-a d}}{\sqrt [3]{c} \sqrt [3]{a+b x^3}}+1}{\sqrt{3}}\right )}{\sqrt{3} c^{11/3} (b c-a d)^{4/3}}+\frac{b}{a x^8 \sqrt [3]{a+b x^3} (b c-a d)} \]
[Out]
b/(a*(b*c - a*d)*x^8*(a + b*x^3)^(1/3)) - ((9*b*c - a*d)*(a + b*x^3)^(2/3))/(8*a^2*c*(b*c - a*d)*x^8) + ((9*b*
c - 4*a*d)*(3*b*c + a*d)*(a + b*x^3)^(2/3))/(20*a^3*c^2*(b*c - a*d)*x^5) - ((81*b^3*c^3 - 9*a*b^2*c^2*d - 12*a
^2*b*c*d^2 - 20*a^3*d^3)*(a + b*x^3)^(2/3))/(40*a^4*c^3*(b*c - a*d)*x^2) + (d^4*ArcTan[(1 + (2*(b*c - a*d)^(1/
3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/Sqrt[3]])/(Sqrt[3]*c^(11/3)*(b*c - a*d)^(4/3)) + (d^4*Log[c + d*x^3])/(6*c^
(11/3)*(b*c - a*d)^(4/3)) - (d^4*Log[((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)])/(2*c^(11/3)*(b*c - a*
d)^(4/3))
________________________________________________________________________________________
Rubi [C] time = 8.29549, antiderivative size = 1486, normalized size of antiderivative =
4.23, number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules
used = {511, 510} \[ \text{result too large to display} \]
Warning: Unable to verify antiderivative.
[In]
Int[1/(x^9*(a + b*x^3)^(4/3)*(c + d*x^3)),x]
[Out]
(280*c^6*(a + b*x^3)^2 - 672*c^5*d*x^3*(a + b*x^3)^2 + 3024*c^4*d^2*x^6*(a + b*x^3)^2 + 18144*c^3*d^3*x^9*(a +
b*x^3)^2 + 13608*c^2*d^4*x^12*(a + b*x^3)^2 - 280*c^6*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*
d)*x^3)/(c*(a + b*x^3))] + 672*c^5*d*x^3*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a
+ b*x^3))] - 3024*c^4*d^2*x^6*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]
- 18144*c^3*d^3*x^9*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 13608*c^
2*d^4*x^12*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 66*c^4*(b*c - a*d
)^2*x^6*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 312*c^3*d*(b*c - a*d)^2*x^9*Hyper
geometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 2268*c^2*d^2*(b*c - a*d)^2*x^12*Hypergeometric
2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 6696*c*d^3*(b*c - a*d)^2*x^15*Hypergeometric2F1[2, 7/3,
10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 4050*d^4*(b*c - a*d)^2*x^18*Hypergeometric2F1[2, 7/3, 10/3, ((b*c
- a*d)*x^3)/(c*(a + b*x^3))] + 189*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d
)*x^3)/(c*(a + b*x^3))] - 108*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x
^3)/(c*(a + b*x^3))] - 3618*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*
x^3)/(c*(a + b*x^3))] - 6156*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x
^3)/(c*(a + b*x^3))] - 2835*d^4*(b*c - a*d)^2*x^18*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)
/(c*(a + b*x^3))] + 54*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)
/(c*(a + b*x^3))] - 648*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x
^3)/(c*(a + b*x^3))] - 2268*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c -
a*d)*x^3)/(c*(a + b*x^3))] - 2376*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((
b*c - a*d)*x^3)/(c*(a + b*x^3))] - 810*d^4*(b*c - a*d)^2*x^18*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3},
((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 81*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 1
0/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 324*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1
, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 486*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 2,
2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 324*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ
[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 81*d^4*(b*c - a*d)^2*x^18*Hypergeome
tricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(560*c^6*(b*c - a*d)*x^11*(a +
b*x^3)^(7/3))
Rule 511
Int[((e_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> Dist[(a^IntPa
rt[p]*(a + b*x^n)^FracPart[p])/(1 + (b*x^n)/a)^FracPart[p], Int[(e*x)^m*(1 + (b*x^n)/a)^p*(c + d*x^n)^q, x], x
] /; FreeQ[{a, b, c, d, e, m, n, p, q}, x] && NeQ[b*c - a*d, 0] && NeQ[m, -1] && NeQ[m, n - 1] && !(IntegerQ[
p] || GtQ[a, 0])
Rule 510
Int[((e_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> Simp[(a^p*c^q
*(e*x)^(m + 1)*AppellF1[(m + 1)/n, -p, -q, 1 + (m + 1)/n, -((b*x^n)/a), -((d*x^n)/c)])/(e*(m + 1)), x] /; Free
Q[{a, b, c, d, e, m, n, p, q}, x] && NeQ[b*c - a*d, 0] && NeQ[m, -1] && NeQ[m, n - 1] && (IntegerQ[p] || GtQ[a
, 0]) && (IntegerQ[q] || GtQ[c, 0])
Rubi steps
\begin{align*} \int \frac{1}{x^9 \left (a+b x^3\right )^{4/3} \left (c+d x^3\right )} \, dx &=\frac{\sqrt [3]{1+\frac{b x^3}{a}} \int \frac{1}{x^9 \left (1+\frac{b x^3}{a}\right )^{4/3} \left (c+d x^3\right )} \, dx}{a \sqrt [3]{a+b x^3}}\\ &=\frac{280 c^6 \left (a+b x^3\right )^2-672 c^5 d x^3 \left (a+b x^3\right )^2+3024 c^4 d^2 x^6 \left (a+b x^3\right )^2+18144 c^3 d^3 x^9 \left (a+b x^3\right )^2+13608 c^2 d^4 x^{12} \left (a+b x^3\right )^2-280 c^6 \left (a+b x^3\right )^2 \, _2F_1\left (\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+672 c^5 d x^3 \left (a+b x^3\right )^2 \, _2F_1\left (\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-3024 c^4 d^2 x^6 \left (a+b x^3\right )^2 \, _2F_1\left (\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-18144 c^3 d^3 x^9 \left (a+b x^3\right )^2 \, _2F_1\left (\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-13608 c^2 d^4 x^{12} \left (a+b x^3\right )^2 \, _2F_1\left (\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-66 c^4 (b c-a d)^2 x^6 \, _2F_1\left (2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+312 c^3 d (b c-a d)^2 x^9 \, _2F_1\left (2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-2268 c^2 d^2 (b c-a d)^2 x^{12} \, _2F_1\left (2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-6696 c d^3 (b c-a d)^2 x^{15} \, _2F_1\left (2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-4050 d^4 (b c-a d)^2 x^{18} \, _2F_1\left (2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+189 c^4 (b c-a d)^2 x^6 \, _3F_2\left (2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-108 c^3 d (b c-a d)^2 x^9 \, _3F_2\left (2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-3618 c^2 d^2 (b c-a d)^2 x^{12} \, _3F_2\left (2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-6156 c d^3 (b c-a d)^2 x^{15} \, _3F_2\left (2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-2835 d^4 (b c-a d)^2 x^{18} \, _3F_2\left (2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+54 c^4 (b c-a d)^2 x^6 \, _4F_3\left (2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-648 c^3 d (b c-a d)^2 x^9 \, _4F_3\left (2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-2268 c^2 d^2 (b c-a d)^2 x^{12} \, _4F_3\left (2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-2376 c d^3 (b c-a d)^2 x^{15} \, _4F_3\left (2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-810 d^4 (b c-a d)^2 x^{18} \, _4F_3\left (2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-81 c^4 (b c-a d)^2 x^6 \, _5F_4\left (2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-324 c^3 d (b c-a d)^2 x^9 \, _5F_4\left (2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-486 c^2 d^2 (b c-a d)^2 x^{12} \, _5F_4\left (2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-324 c d^3 (b c-a d)^2 x^{15} \, _5F_4\left (2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-81 d^4 (b c-a d)^2 x^{18} \, _5F_4\left (2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )}{560 c^6 (b c-a d) x^{11} \left (a+b x^3\right )^{7/3}}\\ \end{align*}
Mathematica [C] time = 3.74252, size = 1486, normalized size = 4.23 \[ \text{result too large to display} \]
Warning: Unable to verify antiderivative.
[In]
Integrate[1/(x^9*(a + b*x^3)^(4/3)*(c + d*x^3)),x]
[Out]
(-280*c^6*(a + b*x^3)^2 + 672*c^5*d*x^3*(a + b*x^3)^2 - 3024*c^4*d^2*x^6*(a + b*x^3)^2 - 18144*c^3*d^3*x^9*(a
+ b*x^3)^2 - 13608*c^2*d^4*x^12*(a + b*x^3)^2 + 280*c^6*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a
*d)*x^3)/(c*(a + b*x^3))] - 672*c^5*d*x^3*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a
+ b*x^3))] + 3024*c^4*d^2*x^6*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]
+ 18144*c^3*d^3*x^9*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 13608*c
^2*d^4*x^12*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 66*c^4*(b*c - a*
d)^2*x^6*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 312*c^3*d*(b*c - a*d)^2*x^9*Hype
rgeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 2268*c^2*d^2*(b*c - a*d)^2*x^12*Hypergeometri
c2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 6696*c*d^3*(b*c - a*d)^2*x^15*Hypergeometric2F1[2, 7/3
, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 4050*d^4*(b*c - a*d)^2*x^18*Hypergeometric2F1[2, 7/3, 10/3, ((b*c
- a*d)*x^3)/(c*(a + b*x^3))] - 189*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*
d)*x^3)/(c*(a + b*x^3))] + 108*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*
x^3)/(c*(a + b*x^3))] + 3618*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)
*x^3)/(c*(a + b*x^3))] + 6156*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*
x^3)/(c*(a + b*x^3))] + 2835*d^4*(b*c - a*d)^2*x^18*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3
)/(c*(a + b*x^3))] - 54*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3
)/(c*(a + b*x^3))] + 648*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*
x^3)/(c*(a + b*x^3))] + 2268*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c
- a*d)*x^3)/(c*(a + b*x^3))] + 2376*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, (
(b*c - a*d)*x^3)/(c*(a + b*x^3))] + 810*d^4*(b*c - a*d)^2*x^18*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3},
((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 81*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1,
10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 324*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {
1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 486*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 2
, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 324*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPF
Q[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 81*d^4*(b*c - a*d)^2*x^18*Hypergeom
etricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(560*c^6*(-(b*c) + a*d)*x^11*
(a + b*x^3)^(7/3))
________________________________________________________________________________________
Maple [F] time = 0.066, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{9} \left ( d{x}^{3}+c \right ) } \left ( b{x}^{3}+a \right ) ^{-{\frac{4}{3}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x)
[Out]
int(1/x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x)
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{4}{3}}{\left (d x^{3} + c\right )} x^{9}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm="maxima")
[Out]
integrate(1/((b*x^3 + a)^(4/3)*(d*x^3 + c)*x^9), x)
________________________________________________________________________________________
Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm="fricas")
[Out]
Timed out
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x**9/(b*x**3+a)**(4/3)/(d*x**3+c),x)
[Out]
Timed out
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{4}{3}}{\left (d x^{3} + c\right )} x^{9}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm="giac")
[Out]
integrate(1/((b*x^3 + a)^(4/3)*(d*x^3 + c)*x^9), x)