3.708 \(\int \frac{(a+b x^3)^{4/3}}{x^{14} (c+d x^3)} \, dx\)

Optimal. Leaf size=392 \[ -\frac{\sqrt [3]{a+b x^3} \left (260 a^2 b^2 c^2 d^2-2275 a^3 b c d^3+1820 a^4 d^4+78 a b^3 c^3 d+36 b^4 c^4\right )}{1820 a^3 c^5 x}+\frac{\sqrt [3]{a+b x^3} \left (-520 a^2 b c d^2+455 a^3 d^3+26 a b^2 c^2 d+12 b^3 c^3\right )}{1820 a^2 c^4 x^4}-\frac{\sqrt [3]{a+b x^3} \left (130 a^2 d^2-143 a b c d+4 b^2 c^2\right )}{910 a c^3 x^7}-\frac{d^3 (b c-a d)^{4/3} \log \left (c+d x^3\right )}{6 c^{16/3}}+\frac{d^3 (b c-a d)^{4/3} \log \left (\frac{x \sqrt [3]{b c-a d}}{\sqrt [3]{c}}-\sqrt [3]{a+b x^3}\right )}{2 c^{16/3}}+\frac{d^3 (b c-a d)^{4/3} \tan ^{-1}\left (\frac{\frac{2 x \sqrt [3]{b c-a d}}{\sqrt [3]{c} \sqrt [3]{a+b x^3}}+1}{\sqrt{3}}\right )}{\sqrt{3} c^{16/3}}-\frac{\sqrt [3]{a+b x^3} (14 b c-13 a d)}{130 c^2 x^{10}}-\frac{a \sqrt [3]{a+b x^3}}{13 c x^{13}} \]

[Out]

-(a*(a + b*x^3)^(1/3))/(13*c*x^13) - ((14*b*c - 13*a*d)*(a + b*x^3)^(1/3))/(130*c^2*x^10) - ((4*b^2*c^2 - 143*
a*b*c*d + 130*a^2*d^2)*(a + b*x^3)^(1/3))/(910*a*c^3*x^7) + ((12*b^3*c^3 + 26*a*b^2*c^2*d - 520*a^2*b*c*d^2 +
455*a^3*d^3)*(a + b*x^3)^(1/3))/(1820*a^2*c^4*x^4) - ((36*b^4*c^4 + 78*a*b^3*c^3*d + 260*a^2*b^2*c^2*d^2 - 227
5*a^3*b*c*d^3 + 1820*a^4*d^4)*(a + b*x^3)^(1/3))/(1820*a^3*c^5*x) + (d^3*(b*c - a*d)^(4/3)*ArcTan[(1 + (2*(b*c
- a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/Sqrt[3]])/(Sqrt[3]*c^(16/3)) - (d^3*(b*c - a*d)^(4/3)*Log[c + d*
x^3])/(6*c^(16/3)) + (d^3*(b*c - a*d)^(4/3)*Log[((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)])/(2*c^(16/3
))

________________________________________________________________________________________

Rubi [C]  time = 4.39057, antiderivative size = 1446, normalized size of antiderivative = 3.69, 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[(a + b*x^3)^(4/3)/(x^14*(c + d*x^3)),x]

[Out]

-(140*a^2*c^5 + 840*a*b*c^5*x^3 - 686*a^2*c^4*d*x^3 + 700*b^2*c^5*x^6 - 1316*a*b*c^4*d*x^6 + 612*a^2*c^3*d^2*x
^6 - 630*b^2*c^4*d*x^9 + 1152*a*b*c^3*d^2*x^9 - 513*a^2*c^2*d^3*x^9 + 540*b^2*c^3*d^2*x^12 - 918*a*b*c^2*d^3*x
^12 + 324*a^2*c*d^4*x^12 - 405*b^2*c^2*d^3*x^15 + 324*a*b*c*d^4*x^15 - 828*a*b*c^5*x^3*Hypergeometric2F1[-1/3,
2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 828*a^2*c^4*d*x^3*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x
^3)/(c*(a + b*x^3))] - 828*b^2*c^5*x^6*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 91
8*a*b*c^4*d*x^6*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 90*a^2*c^3*d^2*x^6*Hyperg
eometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 90*b^2*c^4*d*x^9*Hypergeometric2F1[-1/3, 2, 2/3
, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 234*a*b*c^3*d^2*x^9*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(
c*(a + b*x^3))] - 324*a^2*c^2*d^3*x^9*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 324
*b^2*c^3*d^2*x^12*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 918*a*b*c^2*d^3*x^12*Hy
pergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 594*a^2*c*d^4*x^12*Hypergeometric2F1[-1/3,
2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 594*b^2*c^2*d^3*x^15*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)
*x^3)/(c*(a + b*x^3))] + 594*a*b*c*d^4*x^15*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]
- 280*b^2*c^5*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 560*a*b*c^4*d*x^6*Hyper
geometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 280*a^2*c^3*d^2*x^6*Hypergeometric2F1[2/3, 1, 5
/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 252*b^2*c^4*d*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c
*(a + b*x^3))] - 504*a*b*c^3*d^2*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 252*a
^2*c^2*d^3*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 216*b^2*c^3*d^2*x^12*Hyperg
eometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 432*a*b*c^2*d^3*x^12*Hypergeometric2F1[2/3, 1, 5
/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 216*a^2*c*d^4*x^12*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(
c*(a + b*x^3))] + 162*b^2*c^2*d^3*x^15*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 324
*a*b*c*d^4*x^15*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 162*a^2*d^5*x^15*Hypergeom
etric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 54*c*(b*c - a*d)*x^3*(a + b*x^3)*(7*c - 6*d*x^3)*(c
+ d*x^3)^2*HypergeometricPFQ[{-1/3, 2, 2}, {2/3, 1}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 54*c*(b*c - a*d)*x^
3*(a + b*x^3)*(c + d*x^3)^3*HypergeometricPFQ[{-1/3, 2, 2, 2}, {2/3, 1, 1}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]
)/(1820*c^6*x^13*(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{\left (a+b x^3\right )^{4/3}}{x^{14} \left (c+d x^3\right )} \, dx &=\frac{\left (a \sqrt [3]{a+b x^3}\right ) \int \frac{\left (1+\frac{b x^3}{a}\right )^{4/3}}{x^{14} \left (c+d x^3\right )} \, dx}{\sqrt [3]{1+\frac{b x^3}{a}}}\\ &=-\frac{140 a^2 c^5+840 a b c^5 x^3-686 a^2 c^4 d x^3+700 b^2 c^5 x^6-1316 a b c^4 d x^6+612 a^2 c^3 d^2 x^6-630 b^2 c^4 d x^9+1152 a b c^3 d^2 x^9-513 a^2 c^2 d^3 x^9+540 b^2 c^3 d^2 x^{12}-918 a b c^2 d^3 x^{12}+324 a^2 c d^4 x^{12}-405 b^2 c^2 d^3 x^{15}+324 a b c d^4 x^{15}-828 a b c^5 x^3 \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+828 a^2 c^4 d x^3 \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-828 b^2 c^5 x^6 \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+918 a b c^4 d x^6 \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-90 a^2 c^3 d^2 x^6 \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+90 b^2 c^4 d x^9 \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+234 a b c^3 d^2 x^9 \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-324 a^2 c^2 d^3 x^9 \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+324 b^2 c^3 d^2 x^{12} \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-918 a b c^2 d^3 x^{12} \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+594 a^2 c d^4 x^{12} \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-594 b^2 c^2 d^3 x^{15} \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )+594 a b c d^4 x^{15} \, _2F_1\left (-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-280 b^2 c^5 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 )+560 a b c^4 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 )-280 a^2 c^3 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 )+252 b^2 c^4 d 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 )-504 a b c^3 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 )+252 a^2 c^2 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 )-216 b^2 c^3 d^2 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 )+432 a b c^2 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 )-216 a^2 c 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 )+162 b^2 c^2 d^3 x^{15} \, _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 )-324 a b c d^4 x^{15} \, _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^2 d^5 x^{15} \, _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 c (b c-a d) x^3 \left (a+b x^3\right ) \left (7 c-6 d x^3\right ) \left (c+d x^3\right )^2 \, _3F_2\left (-\frac{1}{3},2,2;\frac{2}{3},1;\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-54 c (b c-a d) x^3 \left (a+b x^3\right ) \left (c+d x^3\right )^3 \, _4F_3\left (-\frac{1}{3},2,2,2;\frac{2}{3},1,1;\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )}{1820 c^6 x^{13} \left (a+b x^3\right )^{2/3}}\\ \end{align*}

Mathematica [C]  time = 3.91673, size = 1446, normalized size = 3.69 \[ \text{result too large to display} \]

Warning: Unable to verify antiderivative.

[In]

Integrate[(a + b*x^3)^(4/3)/(x^14*(c + d*x^3)),x]

[Out]

(-140*a^2*c^5 - 840*a*b*c^5*x^3 + 686*a^2*c^4*d*x^3 - 700*b^2*c^5*x^6 + 1316*a*b*c^4*d*x^6 - 612*a^2*c^3*d^2*x
^6 + 630*b^2*c^4*d*x^9 - 1152*a*b*c^3*d^2*x^9 + 513*a^2*c^2*d^3*x^9 - 540*b^2*c^3*d^2*x^12 + 918*a*b*c^2*d^3*x
^12 - 324*a^2*c*d^4*x^12 + 405*b^2*c^2*d^3*x^15 - 324*a*b*c*d^4*x^15 + 828*a*b*c^5*x^3*Hypergeometric2F1[-1/3,
2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 828*a^2*c^4*d*x^3*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x
^3)/(c*(a + b*x^3))] + 828*b^2*c^5*x^6*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 91
8*a*b*c^4*d*x^6*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 90*a^2*c^3*d^2*x^6*Hyperg
eometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 90*b^2*c^4*d*x^9*Hypergeometric2F1[-1/3, 2, 2/3
, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 234*a*b*c^3*d^2*x^9*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(
c*(a + b*x^3))] + 324*a^2*c^2*d^3*x^9*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 324
*b^2*c^3*d^2*x^12*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 918*a*b*c^2*d^3*x^12*Hy
pergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 594*a^2*c*d^4*x^12*Hypergeometric2F1[-1/3,
2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 594*b^2*c^2*d^3*x^15*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)
*x^3)/(c*(a + b*x^3))] - 594*a*b*c*d^4*x^15*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]
+ 280*b^2*c^5*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 560*a*b*c^4*d*x^6*Hyper
geometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 280*a^2*c^3*d^2*x^6*Hypergeometric2F1[2/3, 1, 5
/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 252*b^2*c^4*d*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c
*(a + b*x^3))] + 504*a*b*c^3*d^2*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 252*a
^2*c^2*d^3*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 216*b^2*c^3*d^2*x^12*Hyperg
eometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 432*a*b*c^2*d^3*x^12*Hypergeometric2F1[2/3, 1, 5
/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 216*a^2*c*d^4*x^12*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(
c*(a + b*x^3))] - 162*b^2*c^2*d^3*x^15*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 324
*a*b*c*d^4*x^15*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 162*a^2*d^5*x^15*Hypergeom
etric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 54*c*(b*c - a*d)*x^3*(a + b*x^3)*(c + d*x^3)^2*(-7*
c + 6*d*x^3)*HypergeometricPFQ[{-1/3, 2, 2}, {2/3, 1}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 54*c*(b*c - a*d)*x
^3*(a + b*x^3)*(c + d*x^3)^3*HypergeometricPFQ[{-1/3, 2, 2, 2}, {2/3, 1, 1}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))
])/(1820*c^6*x^13*(a + b*x^3)^(2/3))

________________________________________________________________________________________

Maple [F]  time = 0.063, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{14} \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((b*x^3+a)^(4/3)/x^14/(d*x^3+c),x)

[Out]

int((b*x^3+a)^(4/3)/x^14/(d*x^3+c),x)

________________________________________________________________________________________

Maxima [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b x^{3} + a\right )}^{\frac{4}{3}}}{{\left (d x^{3} + c\right )} x^{14}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^3+a)^(4/3)/x^14/(d*x^3+c),x, algorithm="maxima")

[Out]

integrate((b*x^3 + a)^(4/3)/((d*x^3 + c)*x^14), 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((b*x^3+a)^(4/3)/x^14/(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((b*x**3+a)**(4/3)/x**14/(d*x**3+c),x)

[Out]

Timed out

________________________________________________________________________________________

Giac [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b x^{3} + a\right )}^{\frac{4}{3}}}{{\left (d x^{3} + c\right )} x^{14}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^3+a)^(4/3)/x^14/(d*x^3+c),x, algorithm="giac")

[Out]

integrate((b*x^3 + a)^(4/3)/((d*x^3 + c)*x^14), x)