3.116 \(\int \frac{1}{(a+b x^3)^{7/3} (c+d x^3)^3} \, dx\)

Optimal. Leaf size=463 \[ \frac{d x \left (a+b x^3\right )^{2/3} \left (-42 a^2 b c d^2+10 a^3 d^3-135 a b^2 c^2 d+27 b^3 c^3\right )}{36 a^2 c^2 \left (c+d x^3\right ) (b c-a d)^4}+\frac{b x \left (-2 a^2 d^2-42 a b c d+9 b^2 c^2\right )}{12 a^2 c \sqrt [3]{a+b x^3} \left (c+d x^3\right ) (b c-a d)^3}+\frac{d^2 \left (5 a^2 d^2-24 a b c d+54 b^2 c^2\right ) \log \left (c+d x^3\right )}{54 c^{8/3} (b c-a d)^{13/3}}-\frac{d^2 \left (5 a^2 d^2-24 a b c d+54 b^2 c^2\right ) \log \left (\frac{x \sqrt [3]{b c-a d}}{\sqrt [3]{c}}-\sqrt [3]{a+b x^3}\right )}{18 c^{8/3} (b c-a d)^{13/3}}+\frac{d^2 \left (5 a^2 d^2-24 a b c d+54 b^2 c^2\right ) \tan ^{-1}\left (\frac{\frac{2 x \sqrt [3]{b c-a d}}{\sqrt [3]{c} \sqrt [3]{a+b x^3}}+1}{\sqrt{3}}\right )}{9 \sqrt{3} c^{8/3} (b c-a d)^{13/3}}-\frac{d x}{6 c \left (a+b x^3\right )^{4/3} \left (c+d x^3\right )^2 (b c-a d)}+\frac{b x (2 a d+3 b c)}{12 a c \left (a+b x^3\right )^{4/3} \left (c+d x^3\right ) (b c-a d)^2} \]

[Out]

-(d*x)/(6*c*(b*c - a*d)*(a + b*x^3)^(4/3)*(c + d*x^3)^2) + (b*(3*b*c + 2*a*d)*x)/(12*a*c*(b*c - a*d)^2*(a + b*
x^3)^(4/3)*(c + d*x^3)) + (b*(9*b^2*c^2 - 42*a*b*c*d - 2*a^2*d^2)*x)/(12*a^2*c*(b*c - a*d)^3*(a + b*x^3)^(1/3)
*(c + d*x^3)) + (d*(27*b^3*c^3 - 135*a*b^2*c^2*d - 42*a^2*b*c*d^2 + 10*a^3*d^3)*x*(a + b*x^3)^(2/3))/(36*a^2*c
^2*(b*c - a*d)^4*(c + d*x^3)) + (d^2*(54*b^2*c^2 - 24*a*b*c*d + 5*a^2*d^2)*ArcTan[(1 + (2*(b*c - a*d)^(1/3)*x)
/(c^(1/3)*(a + b*x^3)^(1/3)))/Sqrt[3]])/(9*Sqrt[3]*c^(8/3)*(b*c - a*d)^(13/3)) + (d^2*(54*b^2*c^2 - 24*a*b*c*d
+ 5*a^2*d^2)*Log[c + d*x^3])/(54*c^(8/3)*(b*c - a*d)^(13/3)) - (d^2*(54*b^2*c^2 - 24*a*b*c*d + 5*a^2*d^2)*Log
[((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)])/(18*c^(8/3)*(b*c - a*d)^(13/3))

________________________________________________________________________________________

Rubi [C]  time = 8.66242, antiderivative size = 1990, normalized size of antiderivative = 4.3, number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095, Rules used = {430, 429} \[ \text{result too large to display} \]

Warning: Unable to verify antiderivative.

[In]

Int[1/((a + b*x^3)^(7/3)*(c + d*x^3)^3),x]

[Out]

-(522756*c^6*(b*c - a*d)^3*x^9*(a + b*x^3)^2 + 1516320*c^5*d*(b*c - a*d)^3*x^12*(a + b*x^3)^2 + 2198664*c^4*d^
2*(b*c - a*d)^3*x^15*(a + b*x^3)^2 + 1415232*c^3*d^3*(b*c - a*d)^3*x^18*(a + b*x^3)^2 + 341172*c^2*d^4*(b*c -
a*d)^3*x^21*(a + b*x^3)^2 + 28042560*c^7*(b*c - a*d)^2*x^6*(a + b*x^3)^3 + 107602560*c^6*d*(b*c - a*d)^2*x^9*(
a + b*x^3)^3 + 157697280*c^5*d^2*(b*c - a*d)^2*x^12*(a + b*x^3)^3 + 101088000*c^4*d^3*(b*c - a*d)^2*x^15*(a +
b*x^3)^3 + 24261120*c^3*d^4*(b*c - a*d)^2*x^18*(a + b*x^3)^3 - 265470660*c^8*(b*c - a*d)*x^3*(a + b*x^3)^4 - 1
019636800*c^7*d*(b*c - a*d)*x^6*(a + b*x^3)^4 - 1466086440*c^6*d^2*(b*c - a*d)*x^9*(a + b*x^3)^4 - 930252960*c
^5*d^3*(b*c - a*d)*x^12*(a + b*x^3)^4 - 221899860*c^4*d^4*(b*c - a*d)*x^15*(a + b*x^3)^4 + 335877360*c^9*(a +
b*x^3)^5 + 1279532800*c^8*d*x^3*(a + b*x^3)^5 + 1823334240*c^7*d^2*x^6*(a + b*x^3)^5 + 1151579520*c^6*d^3*x^9*
(a + b*x^3)^5 + 273939120*c^5*d^4*x^12*(a + b*x^3)^5 - 67420080*c^7*(b*c - a*d)^2*x^6*(a + b*x^3)^3*Hypergeome
tric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 259692160*c^6*d*(b*c - a*d)^2*x^9*(a + b*x^3)^3*Hype
rgeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 377700960*c^5*d^2*(b*c - a*d)^2*x^12*(a + b*x^
3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 241113600*c^4*d^3*(b*c - a*d)^2*x^15*
(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 57723120*c^3*d^4*(b*c - a*d)
^2*x^18*(a + b*x^3)^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 349440000*c^8*(b*c -
a*d)*x^3*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1339520000*c^7*d*(
b*c - a*d)*x^6*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1921920000*c^
6*d^2*(b*c - a*d)*x^9*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 121814
7840*c^5*d^3*(b*c - a*d)*x^12*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]
+ 290384640*c^4*d^4*(b*c - a*d)*x^15*(a + b*x^3)^4*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*
x^3))] - 335877360*c^9*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 12795
32800*c^8*d*x^3*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 1823334240*c
^7*d^2*x^6*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 1151579520*c^6*d^
3*x^9*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 273939120*c^5*d^4*x^12
*(a + b*x^3)^5*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 57834*c^4*(b*c - a*d)^5*x^1
5*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 224532*c^3*d*(b*c - a*
d)^5*x^18*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 326592*c^2*d^2
*(b*c - a*d)^5*x^21*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 2109
24*c*d^3*(b*c - a*d)^5*x^24*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))
] - 51030*d^4*(b*c - a*d)^5*x^27*HypergeometricPFQ[{2, 2, 2, 10/3}, {1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*
x^3))] - 5103*c^4*(b*c - a*d)^5*x^15*HypergeometricPFQ[{2, 2, 2, 2, 10/3}, {1, 1, 1, 19/3}, ((b*c - a*d)*x^3)/
(c*(a + b*x^3))] - 20412*c^3*d*(b*c - a*d)^5*x^18*HypergeometricPFQ[{2, 2, 2, 2, 10/3}, {1, 1, 1, 19/3}, ((b*c
- a*d)*x^3)/(c*(a + b*x^3))] - 30618*c^2*d^2*(b*c - a*d)^5*x^21*HypergeometricPFQ[{2, 2, 2, 2, 10/3}, {1, 1,
1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 20412*c*d^3*(b*c - a*d)^5*x^24*HypergeometricPFQ[{2, 2, 2, 2, 1
0/3}, {1, 1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 5103*d^4*(b*c - a*d)^5*x^27*HypergeometricPFQ[{2,
2, 2, 2, 10/3}, {1, 1, 1, 19/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(524160*c^6*(b*c - a*d)^4*x^11*(a + b*x^3
)^(10/3)*(c + d*x^3)^2)

Rule 430

Int[((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> Dist[(a^IntPart[p]*(a + b*x^n)^F
racPart[p])/(1 + (b*x^n)/a)^FracPart[p], Int[(1 + (b*x^n)/a)^p*(c + d*x^n)^q, x], x] /; FreeQ[{a, b, c, d, n,
p, q}, x] && NeQ[b*c - a*d, 0] && NeQ[n, -1] &&  !(IntegerQ[p] || GtQ[a, 0])

Rule 429

Int[((a_) + (b_.)*(x_)^(n_))^(p_)*((c_) + (d_.)*(x_)^(n_))^(q_), x_Symbol] :> Simp[a^p*c^q*x*AppellF1[1/n, -p,
-q, 1 + 1/n, -((b*x^n)/a), -((d*x^n)/c)], x] /; FreeQ[{a, b, c, d, n, p, q}, x] && NeQ[b*c - a*d, 0] && NeQ[n
, -1] && (IntegerQ[p] || GtQ[a, 0]) && (IntegerQ[q] || GtQ[c, 0])

Rubi steps

\begin{align*} \int \frac{1}{\left (a+b x^3\right )^{7/3} \left (c+d x^3\right )^3} \, dx &=\frac{\sqrt [3]{1+\frac{b x^3}{a}} \int \frac{1}{\left (1+\frac{b x^3}{a}\right )^{7/3} \left (c+d x^3\right )^3} \, dx}{a^2 \sqrt [3]{a+b x^3}}\\ &=-\frac{522756 c^6 (b c-a d)^3 x^9 \left (a+b x^3\right )^2+1516320 c^5 d (b c-a d)^3 x^{12} \left (a+b x^3\right )^2+2198664 c^4 d^2 (b c-a d)^3 x^{15} \left (a+b x^3\right )^2+1415232 c^3 d^3 (b c-a d)^3 x^{18} \left (a+b x^3\right )^2+341172 c^2 d^4 (b c-a d)^3 x^{21} \left (a+b x^3\right )^2+28042560 c^7 (b c-a d)^2 x^6 \left (a+b x^3\right )^3+107602560 c^6 d (b c-a d)^2 x^9 \left (a+b x^3\right )^3+157697280 c^5 d^2 (b c-a d)^2 x^{12} \left (a+b x^3\right )^3+101088000 c^4 d^3 (b c-a d)^2 x^{15} \left (a+b x^3\right )^3+24261120 c^3 d^4 (b c-a d)^2 x^{18} \left (a+b x^3\right )^3-265470660 c^8 (b c-a d) x^3 \left (a+b x^3\right )^4-1019636800 c^7 d (b c-a d) x^6 \left (a+b x^3\right )^4-1466086440 c^6 d^2 (b c-a d) x^9 \left (a+b x^3\right )^4-930252960 c^5 d^3 (b c-a d) x^{12} \left (a+b x^3\right )^4-221899860 c^4 d^4 (b c-a d) x^{15} \left (a+b x^3\right )^4+335877360 c^9 \left (a+b x^3\right )^5+1279532800 c^8 d x^3 \left (a+b x^3\right )^5+1823334240 c^7 d^2 x^6 \left (a+b x^3\right )^5+1151579520 c^6 d^3 x^9 \left (a+b x^3\right )^5+273939120 c^5 d^4 x^{12} \left (a+b x^3\right )^5-67420080 c^7 (b c-a d)^2 x^6 \left (a+b x^3\right )^3 \, _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 )-259692160 c^6 d (b c-a d)^2 x^9 \left (a+b x^3\right )^3 \, _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 )-377700960 c^5 d^2 (b c-a d)^2 x^{12} \left (a+b x^3\right )^3 \, _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 )-241113600 c^4 d^3 (b c-a d)^2 x^{15} \left (a+b x^3\right )^3 \, _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 )-57723120 c^3 d^4 (b c-a d)^2 x^{18} \left (a+b x^3\right )^3 \, _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 )[phone] c^8 (b c-a d) x^3 \left (a+b x^3\right )^4 \, _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 )[phone] c^7 d (b c-a d) x^6 \left (a+b x^3\right )^4 \, _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 )[phone] c^6 d^2 (b c-a d) x^9 \left (a+b x^3\right )^4 \, _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 )[phone] c^5 d^3 (b c-a d) x^{12} \left (a+b x^3\right )^4 \, _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 )[phone] c^4 d^4 (b c-a d) x^{15} \left (a+b x^3\right )^4 \, _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 )-335877360 c^9 \left (a+b x^3\right )^5 \, _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 )-1279532800 c^8 d x^3 \left (a+b x^3\right )^5 \, _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 )-1823334240 c^7 d^2 x^6 \left (a+b x^3\right )^5 \, _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 )-1151579520 c^6 d^3 x^9 \left (a+b x^3\right )^5 \, _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 )-273939120 c^5 d^4 x^{12} \left (a+b x^3\right )^5 \, _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 )-57834 c^4 (b c-a d)^5 x^{15} \, _4F_3\left (2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-224532 c^3 d (b c-a d)^5 x^{18} \, _4F_3\left (2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-326592 c^2 d^2 (b c-a d)^5 x^{21} \, _4F_3\left (2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-210924 c d^3 (b c-a d)^5 x^{24} \, _4F_3\left (2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-51030 d^4 (b c-a d)^5 x^{27} \, _4F_3\left (2,2,2,\frac{10}{3};1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-5103 c^4 (b c-a d)^5 x^{15} \, _5F_4\left (2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-20412 c^3 d (b c-a d)^5 x^{18} \, _5F_4\left (2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-30618 c^2 d^2 (b c-a d)^5 x^{21} \, _5F_4\left (2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-20412 c d^3 (b c-a d)^5 x^{24} \, _5F_4\left (2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )-5103 d^4 (b c-a d)^5 x^{27} \, _5F_4\left (2,2,2,2,\frac{10}{3};1,1,1,\frac{19}{3};\frac{(b c-a d) x^3}{c \left (a+b x^3\right )}\right )}{524160 c^6 (b c-a d)^4 x^{11} \left (a+b x^3\right )^{10/3} \left (c+d x^3\right )^2}\\ \end{align*}

Mathematica [A]  time = 5.84791, size = 337, normalized size = 0.73 \[ \frac{1}{36} x \left (a+b x^3\right )^{2/3} \left (\frac{27 b^3 (b c-5 a d)}{a^2 \left (a+b x^3\right ) (b c-a d)^4}-\frac{9 b^3}{a \left (a+b x^3\right )^2 (a d-b c)^3}+\frac{2 d^3 (5 a d-21 b c)}{c^2 \left (c+d x^3\right ) (b c-a d)^4}-\frac{6 d^3}{c \left (c+d x^3\right )^2 (b c-a d)^3}\right )+\frac{d^2 \left (5 a^2 d^2-24 a b c d+54 b^2 c^2\right ) \left (\log \left (\frac{x^2 (b c-a d)^{2/3}}{\left (a x^3+b\right )^{2/3}}+\frac{\sqrt [3]{c} x \sqrt [3]{b c-a d}}{\sqrt [3]{a x^3+b}}+c^{2/3}\right )-2 \log \left (\sqrt [3]{c}-\frac{x \sqrt [3]{b c-a d}}{\sqrt [3]{a x^3+b}}\right )+2 \sqrt{3} \tan ^{-1}\left (\frac{\frac{2 x \sqrt [3]{b c-a d}}{\sqrt [3]{c} \sqrt [3]{a x^3+b}}+1}{\sqrt{3}}\right )\right )}{54 c^{8/3} (b c-a d)^{13/3}} \]

Warning: Unable to verify antiderivative.

[In]

Integrate[1/((a + b*x^3)^(7/3)*(c + d*x^3)^3),x]

[Out]

(x*(a + b*x^3)^(2/3)*((-9*b^3)/(a*(-(b*c) + a*d)^3*(a + b*x^3)^2) + (27*b^3*(b*c - 5*a*d))/(a^2*(b*c - a*d)^4*
(a + b*x^3)) - (6*d^3)/(c*(b*c - a*d)^3*(c + d*x^3)^2) + (2*d^3*(-21*b*c + 5*a*d))/(c^2*(b*c - a*d)^4*(c + d*x
^3))))/36 + (d^2*(54*b^2*c^2 - 24*a*b*c*d + 5*a^2*d^2)*(2*Sqrt[3]*ArcTan[(1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)
*(b + a*x^3)^(1/3)))/Sqrt[3]] - 2*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(b + a*x^3)^(1/3)] + Log[c^(2/3) + ((b*c
- a*d)^(2/3)*x^2)/(b + a*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(b + a*x^3)^(1/3)]))/(54*c^(8/3)*(b*c - a
*d)^(13/3))

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Maple [F]  time = 0.428, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( d{x}^{3}+c \right ) ^{3}} \left ( b{x}^{3}+a \right ) ^{-{\frac{7}{3}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,x)

[Out]

int(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,x)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{7}{3}}{\left (d x^{3} + c\right )}^{3}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,x, algorithm="maxima")

[Out]

integrate(1/((b*x^3 + a)^(7/3)*(d*x^3 + c)^3), 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(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,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(1/(b*x**3+a)**(7/3)/(d*x**3+c)**3,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{7}{3}}{\left (d x^{3} + c\right )}^{3}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,x, algorithm="giac")

[Out]

integrate(1/((b*x^3 + a)^(7/3)*(d*x^3 + c)^3), x)