Optimal. Leaf size=384 \[ \frac{x^2 \left (6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right )}{2 b^6}+\frac{a x^2 \left (13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right )}{9 b^6 \left (a+b x^3\right )}-\frac{a^2 x^2 \left (a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right )}{6 b^6 \left (a+b x^3\right )^2}-\frac{a^{2/3} \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right ) \left (77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right )}{54 b^{20/3}}+\frac{a^{2/3} \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \left (77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right )}{27 b^{20/3}}+\frac{a^{2/3} \tan ^{-1}\left (\frac{\sqrt [3]{a}-2 \sqrt [3]{b} x}{\sqrt{3} \sqrt [3]{a}}\right ) \left (77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right )}{9 \sqrt{3} b^{20/3}}+\frac{x^5 \left (6 a^2 f-3 a b e+b^2 d\right )}{5 b^5}+\frac{x^8 (b e-3 a f)}{8 b^4}+\frac{f x^{11}}{11 b^3} \]
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Rubi [A] time = 1.05046, antiderivative size = 384, normalized size of antiderivative = 1., number of steps used = 14, number of rules used = 10, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {1828, 1851, 1836, 1488, 292, 31, 634, 617, 204, 628} \[ \frac{x^2 \left (6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right )}{2 b^6}+\frac{a x^2 \left (13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right )}{9 b^6 \left (a+b x^3\right )}-\frac{a^2 x^2 \left (a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right )}{6 b^6 \left (a+b x^3\right )^2}-\frac{a^{2/3} \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right ) \left (77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right )}{54 b^{20/3}}+\frac{a^{2/3} \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \left (77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right )}{27 b^{20/3}}+\frac{a^{2/3} \tan ^{-1}\left (\frac{\sqrt [3]{a}-2 \sqrt [3]{b} x}{\sqrt{3} \sqrt [3]{a}}\right ) \left (77 a^2 b e-119 a^3 f-44 a b^2 d+20 b^3 c\right )}{9 \sqrt{3} b^{20/3}}+\frac{x^5 \left (6 a^2 f-3 a b e+b^2 d\right )}{5 b^5}+\frac{x^8 (b e-3 a f)}{8 b^4}+\frac{f x^{11}}{11 b^3} \]
Antiderivative was successfully verified.
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Rule 1828
Rule 1851
Rule 1836
Rule 1488
Rule 292
Rule 31
Rule 634
Rule 617
Rule 204
Rule 628
Rubi steps
\begin{align*} \int \frac{x^{10} \left (c+d x^3+e x^6+f x^9\right )}{\left (a+b x^3\right )^3} \, dx &=-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}-\frac{\int \frac{-2 a^3 b \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x+6 a^2 b^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^4-6 a b^3 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^7-6 a b^4 \left (b^2 d-a b e+a^2 f\right ) x^{10}-6 a b^5 (b e-a f) x^{13}-6 a b^6 f x^{16}}{\left (a+b x^3\right )^2} \, dx}{6 a b^7}\\ &=-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}-\frac{\int \frac{x \left (-2 a^3 b \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right )+6 a^2 b^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^3-6 a b^3 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^6-6 a b^4 \left (b^2 d-a b e+a^2 f\right ) x^9-6 a b^5 (b e-a f) x^{12}-6 a b^6 f x^{15}\right )}{\left (a+b x^3\right )^2} \, dx}{6 a b^7}\\ &=-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{\int \frac{-2 a^3 b^7 \left (11 b^3 c-17 a b^2 d+23 a^2 b e-29 a^3 f\right ) x+18 a^2 b^8 \left (b^3 c-2 a b^2 d+3 a^2 b e-4 a^3 f\right ) x^4+18 a^2 b^9 \left (b^2 d-2 a b e+3 a^2 f\right ) x^7+18 a^2 b^{10} (b e-2 a f) x^{10}+18 a^2 b^{11} f x^{13}}{a+b x^3} \, dx}{18 a^2 b^{13}}\\ &=-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{\int \frac{x \left (-2 a^3 b^7 \left (11 b^3 c-17 a b^2 d+23 a^2 b e-29 a^3 f\right )+18 a^2 b^8 \left (b^3 c-2 a b^2 d+3 a^2 b e-4 a^3 f\right ) x^3+18 a^2 b^9 \left (b^2 d-2 a b e+3 a^2 f\right ) x^6+18 a^2 b^{10} (b e-2 a f) x^9+18 a^2 b^{11} f x^{12}\right )}{a+b x^3} \, dx}{18 a^2 b^{13}}\\ &=\frac{f x^{11}}{11 b^3}-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{\int \frac{x \left (-22 a^3 b^8 \left (11 b^3 c-17 a b^2 d+23 a^2 b e-29 a^3 f\right )+198 a^2 b^9 \left (b^3 c-2 a b^2 d+3 a^2 b e-4 a^3 f\right ) x^3+198 a^2 b^{10} \left (b^2 d-2 a b e+3 a^2 f\right ) x^6+198 a^2 b^{11} (b e-3 a f) x^9\right )}{a+b x^3} \, dx}{198 a^2 b^{14}}\\ &=\frac{(b e-3 a f) x^8}{8 b^4}+\frac{f x^{11}}{11 b^3}-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{\int \frac{x \left (-176 a^3 b^9 \left (11 b^3 c-17 a b^2 d+23 a^2 b e-29 a^3 f\right )+1584 a^2 b^{10} \left (b^3 c-2 a b^2 d+3 a^2 b e-4 a^3 f\right ) x^3+1584 a^2 b^{11} \left (b^2 d-3 a b e+6 a^2 f\right ) x^6\right )}{a+b x^3} \, dx}{1584 a^2 b^{15}}\\ &=\frac{(b e-3 a f) x^8}{8 b^4}+\frac{f x^{11}}{11 b^3}-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{\int \left (1584 a^2 b^9 \left (b^3 c-3 a b^2 d+6 a^2 b e-10 a^3 f\right ) x+1584 a^2 b^{10} \left (b^2 d-3 a b e+6 a^2 f\right ) x^4+\frac{176 \left (-20 a^3 b^{12} c+44 a^4 b^{11} d-77 a^5 b^{10} e+119 a^6 b^9 f\right ) x}{a+b x^3}\right ) \, dx}{1584 a^2 b^{15}}\\ &=\frac{\left (b^3 c-3 a b^2 d+6 a^2 b e-10 a^3 f\right ) x^2}{2 b^6}+\frac{\left (b^2 d-3 a b e+6 a^2 f\right ) x^5}{5 b^5}+\frac{(b e-3 a f) x^8}{8 b^4}+\frac{f x^{11}}{11 b^3}-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}-\frac{\left (a \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right )\right ) \int \frac{x}{a+b x^3} \, dx}{9 b^6}\\ &=\frac{\left (b^3 c-3 a b^2 d+6 a^2 b e-10 a^3 f\right ) x^2}{2 b^6}+\frac{\left (b^2 d-3 a b e+6 a^2 f\right ) x^5}{5 b^5}+\frac{(b e-3 a f) x^8}{8 b^4}+\frac{f x^{11}}{11 b^3}-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{\left (a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right )\right ) \int \frac{1}{\sqrt [3]{a}+\sqrt [3]{b} x} \, dx}{27 b^{19/3}}-\frac{\left (a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right )\right ) \int \frac{\sqrt [3]{a}+\sqrt [3]{b} x}{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2} \, dx}{27 b^{19/3}}\\ &=\frac{\left (b^3 c-3 a b^2 d+6 a^2 b e-10 a^3 f\right ) x^2}{2 b^6}+\frac{\left (b^2 d-3 a b e+6 a^2 f\right ) x^5}{5 b^5}+\frac{(b e-3 a f) x^8}{8 b^4}+\frac{f x^{11}}{11 b^3}-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right ) \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{27 b^{20/3}}-\frac{\left (a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right )\right ) \int \frac{-\sqrt [3]{a} \sqrt [3]{b}+2 b^{2/3} x}{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2} \, dx}{54 b^{20/3}}-\frac{\left (a \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right )\right ) \int \frac{1}{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2} \, dx}{18 b^{19/3}}\\ &=\frac{\left (b^3 c-3 a b^2 d+6 a^2 b e-10 a^3 f\right ) x^2}{2 b^6}+\frac{\left (b^2 d-3 a b e+6 a^2 f\right ) x^5}{5 b^5}+\frac{(b e-3 a f) x^8}{8 b^4}+\frac{f x^{11}}{11 b^3}-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right ) \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{27 b^{20/3}}-\frac{a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right ) \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right )}{54 b^{20/3}}-\frac{\left (a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right )\right ) \operatorname{Subst}\left (\int \frac{1}{-3-x^2} \, dx,x,1-\frac{2 \sqrt [3]{b} x}{\sqrt [3]{a}}\right )}{9 b^{20/3}}\\ &=\frac{\left (b^3 c-3 a b^2 d+6 a^2 b e-10 a^3 f\right ) x^2}{2 b^6}+\frac{\left (b^2 d-3 a b e+6 a^2 f\right ) x^5}{5 b^5}+\frac{(b e-3 a f) x^8}{8 b^4}+\frac{f x^{11}}{11 b^3}-\frac{a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{6 b^6 \left (a+b x^3\right )^2}+\frac{a \left (7 b^3 c-10 a b^2 d+13 a^2 b e-16 a^3 f\right ) x^2}{9 b^6 \left (a+b x^3\right )}+\frac{a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right ) \tan ^{-1}\left (\frac{\sqrt [3]{a}-2 \sqrt [3]{b} x}{\sqrt{3} \sqrt [3]{a}}\right )}{9 \sqrt{3} b^{20/3}}+\frac{a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right ) \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{27 b^{20/3}}-\frac{a^{2/3} \left (20 b^3 c-44 a b^2 d+77 a^2 b e-119 a^3 f\right ) \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right )}{54 b^{20/3}}\\ \end{align*}
Mathematica [A] time = 0.402336, size = 380, normalized size = 0.99 \[ \frac{x^2 \left (6 a^2 b e-10 a^3 f-3 a b^2 d+b^3 c\right )}{2 b^6}+\frac{a x^2 \left (13 a^2 b e-16 a^3 f-10 a b^2 d+7 b^3 c\right )}{9 b^6 \left (a+b x^3\right )}+\frac{a^2 x^2 \left (-a^2 b e+a^3 f+a b^2 d-b^3 c\right )}{6 b^6 \left (a+b x^3\right )^2}+\frac{a^{2/3} \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right ) \left (-77 a^2 b e+119 a^3 f+44 a b^2 d-20 b^3 c\right )}{54 b^{20/3}}-\frac{a^{2/3} \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \left (-77 a^2 b e+119 a^3 f+44 a b^2 d-20 b^3 c\right )}{27 b^{20/3}}-\frac{a^{2/3} \tan ^{-1}\left (\frac{1-\frac{2 \sqrt [3]{b} x}{\sqrt [3]{a}}}{\sqrt{3}}\right ) \left (-77 a^2 b e+119 a^3 f+44 a b^2 d-20 b^3 c\right )}{9 \sqrt{3} b^{20/3}}+\frac{x^5 \left (6 a^2 f-3 a b e+b^2 d\right )}{5 b^5}+\frac{x^8 (b e-3 a f)}{8 b^4}+\frac{f x^{11}}{11 b^3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.013, size = 668, normalized size = 1.7 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35236, size = 1496, normalized size = 3.9 \begin{align*} \frac{1080 \, b^{5} f x^{17} + 135 \,{\left (11 \, b^{5} e - 17 \, a b^{4} f\right )} x^{14} + 54 \,{\left (44 \, b^{5} d - 77 \, a b^{4} e + 119 \, a^{2} b^{3} f\right )} x^{11} + 297 \,{\left (20 \, b^{5} c - 44 \, a b^{4} d + 77 \, a^{2} b^{3} e - 119 \, a^{3} b^{2} f\right )} x^{8} + 1056 \,{\left (20 \, a b^{4} c - 44 \, a^{2} b^{3} d + 77 \, a^{3} b^{2} e - 119 \, a^{4} b f\right )} x^{5} + 660 \,{\left (20 \, a^{2} b^{3} c - 44 \, a^{3} b^{2} d + 77 \, a^{4} b e - 119 \, a^{5} f\right )} x^{2} - 440 \, \sqrt{3}{\left ({\left (20 \, b^{5} c - 44 \, a b^{4} d + 77 \, a^{2} b^{3} e - 119 \, a^{3} b^{2} f\right )} x^{6} + 20 \, a^{2} b^{3} c - 44 \, a^{3} b^{2} d + 77 \, a^{4} b e - 119 \, a^{5} f + 2 \,{\left (20 \, a b^{4} c - 44 \, a^{2} b^{3} d + 77 \, a^{3} b^{2} e - 119 \, a^{4} b f\right )} x^{3}\right )} \left (-\frac{a^{2}}{b^{2}}\right )^{\frac{1}{3}} \arctan \left (\frac{2 \, \sqrt{3} b x \left (-\frac{a^{2}}{b^{2}}\right )^{\frac{1}{3}} + \sqrt{3} a}{3 \, a}\right ) + 220 \,{\left ({\left (20 \, b^{5} c - 44 \, a b^{4} d + 77 \, a^{2} b^{3} e - 119 \, a^{3} b^{2} f\right )} x^{6} + 20 \, a^{2} b^{3} c - 44 \, a^{3} b^{2} d + 77 \, a^{4} b e - 119 \, a^{5} f + 2 \,{\left (20 \, a b^{4} c - 44 \, a^{2} b^{3} d + 77 \, a^{3} b^{2} e - 119 \, a^{4} b f\right )} x^{3}\right )} \left (-\frac{a^{2}}{b^{2}}\right )^{\frac{1}{3}} \log \left (a x^{2} - b x \left (-\frac{a^{2}}{b^{2}}\right )^{\frac{2}{3}} - a \left (-\frac{a^{2}}{b^{2}}\right )^{\frac{1}{3}}\right ) - 440 \,{\left ({\left (20 \, b^{5} c - 44 \, a b^{4} d + 77 \, a^{2} b^{3} e - 119 \, a^{3} b^{2} f\right )} x^{6} + 20 \, a^{2} b^{3} c - 44 \, a^{3} b^{2} d + 77 \, a^{4} b e - 119 \, a^{5} f + 2 \,{\left (20 \, a b^{4} c - 44 \, a^{2} b^{3} d + 77 \, a^{3} b^{2} e - 119 \, a^{4} b f\right )} x^{3}\right )} \left (-\frac{a^{2}}{b^{2}}\right )^{\frac{1}{3}} \log \left (a x + b \left (-\frac{a^{2}}{b^{2}}\right )^{\frac{2}{3}}\right )}{11880 \,{\left (b^{8} x^{6} + 2 \, a b^{7} x^{3} + a^{2} b^{6}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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Giac [A] time = 1.09179, size = 663, normalized size = 1.73 \begin{align*} \frac{{\left (20 \, a b^{3} c \left (-\frac{a}{b}\right )^{\frac{1}{3}} - 44 \, a^{2} b^{2} d \left (-\frac{a}{b}\right )^{\frac{1}{3}} - 119 \, a^{4} f \left (-\frac{a}{b}\right )^{\frac{1}{3}} + 77 \, a^{3} b \left (-\frac{a}{b}\right )^{\frac{1}{3}} e\right )} \left (-\frac{a}{b}\right )^{\frac{1}{3}} \log \left ({\left | x - \left (-\frac{a}{b}\right )^{\frac{1}{3}} \right |}\right )}{27 \, a b^{6}} + \frac{\sqrt{3}{\left (20 \, \left (-a b^{2}\right )^{\frac{2}{3}} b^{3} c - 44 \, \left (-a b^{2}\right )^{\frac{2}{3}} a b^{2} d - 119 \, \left (-a b^{2}\right )^{\frac{2}{3}} a^{3} f + 77 \, \left (-a b^{2}\right )^{\frac{2}{3}} a^{2} b e\right )} \arctan \left (\frac{\sqrt{3}{\left (2 \, x + \left (-\frac{a}{b}\right )^{\frac{1}{3}}\right )}}{3 \, \left (-\frac{a}{b}\right )^{\frac{1}{3}}}\right )}{27 \, b^{8}} - \frac{{\left (20 \, \left (-a b^{2}\right )^{\frac{2}{3}} b^{3} c - 44 \, \left (-a b^{2}\right )^{\frac{2}{3}} a b^{2} d - 119 \, \left (-a b^{2}\right )^{\frac{2}{3}} a^{3} f + 77 \, \left (-a b^{2}\right )^{\frac{2}{3}} a^{2} b e\right )} \log \left (x^{2} + x \left (-\frac{a}{b}\right )^{\frac{1}{3}} + \left (-\frac{a}{b}\right )^{\frac{2}{3}}\right )}{54 \, b^{8}} + \frac{14 \, a b^{4} c x^{5} - 20 \, a^{2} b^{3} d x^{5} - 32 \, a^{4} b f x^{5} + 26 \, a^{3} b^{2} x^{5} e + 11 \, a^{2} b^{3} c x^{2} - 17 \, a^{3} b^{2} d x^{2} - 29 \, a^{5} f x^{2} + 23 \, a^{4} b x^{2} e}{18 \,{\left (b x^{3} + a\right )}^{2} b^{6}} + \frac{40 \, b^{30} f x^{11} - 165 \, a b^{29} f x^{8} + 55 \, b^{30} x^{8} e + 88 \, b^{30} d x^{5} + 528 \, a^{2} b^{28} f x^{5} - 264 \, a b^{29} x^{5} e + 220 \, b^{30} c x^{2} - 660 \, a b^{29} d x^{2} - 2200 \, a^{3} b^{27} f x^{2} + 1320 \, a^{2} b^{28} x^{2} e}{440 \, b^{33}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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