3.671 \(\int \frac{\sqrt [3]{a+b x^3}}{x^{11} (c+d x^3)} \, dx\)

Optimal. Leaf size=318 \[ -\frac{\sqrt [3]{a+b x^3} \left (35 a^2 b c d^2-140 a^3 d^3+15 a b^2 c^2 d+9 b^3 c^3\right )}{140 a^3 c^4 x}+\frac{\sqrt [3]{a+b x^3} \left (-35 a^2 d^2+5 a b c d+3 b^2 c^2\right )}{140 a^2 c^3 x^4}-\frac{d^3 \sqrt [3]{b c-a d} \log \left (c+d x^3\right )}{6 c^{13/3}}+\frac{d^3 \sqrt [3]{b c-a d} \log \left (\frac{x \sqrt [3]{b c-a d}}{\sqrt [3]{c}}-\sqrt [3]{a+b x^3}\right )}{2 c^{13/3}}+\frac{d^3 \sqrt [3]{b c-a d} \tan ^{-1}\left (\frac{\frac{2 x \sqrt [3]{b c-a d}}{\sqrt [3]{c} \sqrt [3]{a+b x^3}}+1}{\sqrt{3}}\right )}{\sqrt{3} c^{13/3}}-\frac{\sqrt [3]{a+b x^3} (b c-10 a d)}{70 a c^2 x^7}-\frac{\sqrt [3]{a+b x^3}}{10 c x^{10}} \]

[Out]

-(a + b*x^3)^(1/3)/(10*c*x^10) - ((b*c - 10*a*d)*(a + b*x^3)^(1/3))/(70*a*c^2*x^7) + ((3*b^2*c^2 + 5*a*b*c*d -
35*a^2*d^2)*(a + b*x^3)^(1/3))/(140*a^2*c^3*x^4) - ((9*b^3*c^3 + 15*a*b^2*c^2*d + 35*a^2*b*c*d^2 - 140*a^3*d^
3)*(a + b*x^3)^(1/3))/(140*a^3*c^4*x) + (d^3*(b*c - a*d)^(1/3)*ArcTan[(1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a
+ b*x^3)^(1/3)))/Sqrt[3]])/(Sqrt[3]*c^(13/3)) - (d^3*(b*c - a*d)^(1/3)*Log[c + d*x^3])/(6*c^(13/3)) + (d^3*(b
*c - a*d)^(1/3)*Log[((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)])/(2*c^(13/3))

________________________________________________________________________________________

Rubi [C]  time = 2.64184, antiderivative size = 905, normalized size of antiderivative = 2.85, 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} \[ -\frac{-324 b c d^3 x^{12}-162 a d^4 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^{12}+162 b c d^3 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^{12}-297 a d^4 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^{12}+297 b c d^3 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^{12}-324 a c d^3 x^9+108 b c^2 d^2 x^9+54 a c d^3 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^9-54 b c^2 d^2 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^9-81 a c d^3 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^9+81 b c^2 d^2 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^9+108 a c^2 d^2 x^6-72 b c^3 d x^6-36 a c^2 d^2 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^6+36 b c^3 d \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^6+99 a c^2 d^2 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^6-99 b c^3 d \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^6+56 b c^4 x^3-72 a c^3 d x^3-28 b c^4 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+28 a c^3 d \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+117 b c^4 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3-117 a c^3 d \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3-54 (b c-a d) \left (2 c-3 d x^3\right ) \left (d x^3+c\right )^2 \, _3F_2\left (\frac{2}{3},2,2;1,\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+27 (b c-a d) \left (d x^3+c\right )^3 \, _4F_3\left (\frac{2}{3},2,2,2;1,1,\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+56 a c^4}{560 c^5 x^{10} \left (b x^3+a\right )^{2/3}} \]

Warning: Unable to verify antiderivative.

[In]

Int[(a + b*x^3)^(1/3)/(x^11*(c + d*x^3)),x]

[Out]

-(56*a*c^4 + 56*b*c^4*x^3 - 72*a*c^3*d*x^3 - 72*b*c^3*d*x^6 + 108*a*c^2*d^2*x^6 + 108*b*c^2*d^2*x^9 - 324*a*c*
d^3*x^9 - 324*b*c*d^3*x^12 - 28*b*c^4*x^3*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] +
28*a*c^3*d*x^3*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 36*b*c^3*d*x^6*Hypergeometr
ic2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 36*a*c^2*d^2*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c
- a*d)*x^3)/(c*(a + b*x^3))] - 54*b*c^2*d^2*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3
))] + 54*a*c*d^3*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 162*b*c*d^3*x^12*Hype
rgeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 162*a*d^4*x^12*Hypergeometric2F1[2/3, 1, 5/3,
((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 117*b*c^4*x^3*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*
x^3))] - 117*a*c^3*d*x^3*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 99*b*c^3*d*x^6*Hy
pergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 99*a*c^2*d^2*x^6*Hypergeometric2F1[2/3, 2, 5
/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 81*b*c^2*d^2*x^9*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*
(a + b*x^3))] - 81*a*c*d^3*x^9*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 297*b*c*d^3
*x^12*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 297*a*d^4*x^12*Hypergeometric2F1[2/3
, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 54*(b*c - a*d)*x^3*(2*c - 3*d*x^3)*(c + d*x^3)^2*Hypergeometric
PFQ[{2/3, 2, 2}, {1, 5/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*(b*c - a*d)*x^3*(c + d*x^3)^3*Hypergeometri
cPFQ[{2/3, 2, 2, 2}, {1, 1, 5/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(560*c^5*x^10*(a + b*x^3)^(2/3))

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{\sqrt [3]{a+b x^3}}{x^{11} \left (c+d x^3\right )} \, dx &=\frac{\sqrt [3]{a+b x^3} \int \frac{\sqrt [3]{1+\frac{b x^3}{a}}}{x^{11} \left (c+d x^3\right )} \, dx}{\sqrt [3]{1+\frac{b x^3}{a}}}\\ &=-\frac{56 a c^4+56 b c^4 x^3-72 a c^3 d x^3-72 b c^3 d x^6+108 a c^2 d^2 x^6+108 b c^2 d^2 x^9-324 a c d^3 x^9-324 b c d^3 x^{12}-28 b c^4 x^3 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+28 a c^3 d x^3 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+36 b c^3 d x^6 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-36 a c^2 d^2 x^6 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-54 b c^2 d^2 x^9 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+54 a c d^3 x^9 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+162 b c d^3 x^{12} \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-162 a d^4 x^{12} \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+117 b c^4 x^3 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-117 a c^3 d x^3 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-99 b c^3 d x^6 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+99 a c^2 d^2 x^6 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+81 b c^2 d^2 x^9 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-81 a c d^3 x^9 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+297 b c d^3 x^{12} \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-297 a d^4 x^{12} \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-54 (b c-a d) x^3 \left (2 c-3 d x^3\right ) \left (c+d x^3\right )^2 \, _3F_2\left (\frac{2}{3},2,2;1,\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+27 (b c-a d) x^3 \left (c+d x^3\right )^3 \, _4F_3\left (\frac{2}{3},2,2,2;1,1,\frac{5}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )}{560 c^5 x^{10} \left (a+b x^3\right )^{2/3}}\\ \end{align*}

Mathematica [C]  time = 3.79019, size = 905, normalized size = 2.85 \[ -\frac{-324 b c d^3 x^{12}-162 a d^4 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^{12}+162 b c d^3 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^{12}-297 a d^4 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^{12}+297 b c d^3 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^{12}-324 a c d^3 x^9+108 b c^2 d^2 x^9+54 a c d^3 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^9-54 b c^2 d^2 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^9-81 a c d^3 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^9+81 b c^2 d^2 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^9+108 a c^2 d^2 x^6-72 b c^3 d x^6-36 a c^2 d^2 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^6+36 b c^3 d \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^6+99 a c^2 d^2 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^6-99 b c^3 d \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^6+56 b c^4 x^3-72 a c^3 d x^3-28 b c^4 \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+28 a c^3 d \, _2F_1\left (\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+117 b c^4 \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3-117 a c^3 d \, _2F_1\left (\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+54 (b c-a d) \left (d x^3+c\right )^2 \left (3 d x^3-2 c\right ) \text{HypergeometricPFQ}\left (\left \{\frac{2}{3},2,2\right \},\left \{1,\frac{5}{3}\right \},\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+27 (b c-a d) \left (d x^3+c\right )^3 \text{HypergeometricPFQ}\left (\left \{\frac{2}{3},2,2,2\right \},\left \{1,1,\frac{5}{3}\right \},\frac{(b c-a d) x^3}{c \left (b x^3+a\right )}\right ) x^3+56 a c^4}{560 c^5 x^{10} \left (b x^3+a\right )^{2/3}} \]

Warning: Unable to verify antiderivative.

[In]

Integrate[(a + b*x^3)^(1/3)/(x^11*(c + d*x^3)),x]

[Out]

-(56*a*c^4 + 56*b*c^4*x^3 - 72*a*c^3*d*x^3 - 72*b*c^3*d*x^6 + 108*a*c^2*d^2*x^6 + 108*b*c^2*d^2*x^9 - 324*a*c*
d^3*x^9 - 324*b*c*d^3*x^12 - 28*b*c^4*x^3*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] +
28*a*c^3*d*x^3*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 36*b*c^3*d*x^6*Hypergeometr
ic2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 36*a*c^2*d^2*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c
- a*d)*x^3)/(c*(a + b*x^3))] - 54*b*c^2*d^2*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3
))] + 54*a*c*d^3*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 162*b*c*d^3*x^12*Hype
rgeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 162*a*d^4*x^12*Hypergeometric2F1[2/3, 1, 5/3,
((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 117*b*c^4*x^3*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*
x^3))] - 117*a*c^3*d*x^3*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 99*b*c^3*d*x^6*Hy
pergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 99*a*c^2*d^2*x^6*Hypergeometric2F1[2/3, 2, 5
/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 81*b*c^2*d^2*x^9*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*
(a + b*x^3))] - 81*a*c*d^3*x^9*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 297*b*c*d^3
*x^12*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 297*a*d^4*x^12*Hypergeometric2F1[2/3
, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 54*(b*c - a*d)*x^3*(c + d*x^3)^2*(-2*c + 3*d*x^3)*Hypergeometri
cPFQ[{2/3, 2, 2}, {1, 5/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*(b*c - a*d)*x^3*(c + d*x^3)^3*Hypergeometr
icPFQ[{2/3, 2, 2, 2}, {1, 1, 5/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(560*c^5*x^10*(a + b*x^3)^(2/3))

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Maple [F]  time = 0.056, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{11} \left ( d{x}^{3}+c \right ) }\sqrt [3]{b{x}^{3}+a}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x^3+a)^(1/3)/x^11/(d*x^3+c),x)

[Out]

int((b*x^3+a)^(1/3)/x^11/(d*x^3+c),x)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{{\left (d x^{3} + c\right )} x^{11}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^3+a)^(1/3)/x^11/(d*x^3+c),x, algorithm="maxima")

[Out]

integrate((b*x^3 + a)^(1/3)/((d*x^3 + c)*x^11), x)

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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((b*x^3+a)^(1/3)/x^11/(d*x^3+c),x, algorithm="fricas")

[Out]

Timed out

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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((b*x**3+a)**(1/3)/x**11/(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{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{{\left (d x^{3} + c\right )} x^{11}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^3+a)^(1/3)/x^11/(d*x^3+c),x, algorithm="giac")

[Out]

integrate((b*x^3 + a)^(1/3)/((d*x^3 + c)*x^11), x)