Optimal. Leaf size=316 \[ \frac {x^8 \left (a^2 f-a b e+b^2 d\right )}{8 b^3}-\frac {a x^2 \left (a^3 (-f)+a^2 b e-a b^2 d+b^3 c\right )}{2 b^5}+\frac {x^5 \left (a^3 (-f)+a^2 b e-a b^2 d+b^3 c\right )}{5 b^4}+\frac {a^{5/3} \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right ) \left (a^3 (-f)+a^2 b e-a b^2 d+b^3 c\right )}{6 b^{17/3}}-\frac {a^{5/3} \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \left (a^3 (-f)+a^2 b e-a b^2 d+b^3 c\right )}{3 b^{17/3}}-\frac {a^{5/3} \tan ^{-1}\left (\frac {\sqrt [3]{a}-2 \sqrt [3]{b} x}{\sqrt {3} \sqrt [3]{a}}\right ) \left (a^3 (-f)+a^2 b e-a b^2 d+b^3 c\right )}{\sqrt {3} b^{17/3}}+\frac {x^{11} (b e-a f)}{11 b^2}+\frac {f x^{14}}{14 b} \]
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Rubi [A] time = 0.31, antiderivative size = 316, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 8, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.267, Rules used = {1836, 1488, 292, 31, 634, 617, 204, 628} \[ \frac {x^5 \left (a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right )}{5 b^4}-\frac {a x^2 \left (a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right )}{2 b^5}+\frac {a^{5/3} \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right ) \left (a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right )}{6 b^{17/3}}-\frac {a^{5/3} \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \left (a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right )}{3 b^{17/3}}-\frac {a^{5/3} \tan ^{-1}\left (\frac {\sqrt [3]{a}-2 \sqrt [3]{b} x}{\sqrt {3} \sqrt [3]{a}}\right ) \left (a^2 b e+a^3 (-f)-a b^2 d+b^3 c\right )}{\sqrt {3} b^{17/3}}+\frac {x^8 \left (a^2 f-a b e+b^2 d\right )}{8 b^3}+\frac {x^{11} (b e-a f)}{11 b^2}+\frac {f x^{14}}{14 b} \]
Antiderivative was successfully verified.
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Rule 31
Rule 204
Rule 292
Rule 617
Rule 628
Rule 634
Rule 1488
Rule 1836
Rubi steps
\begin {align*} \int \frac {x^7 \left (c+d x^3+e x^6+f x^9\right )}{a+b x^3} \, dx &=\frac {f x^{14}}{14 b}+\frac {\int \frac {x^7 \left (14 b c+14 b d x^3+14 (b e-a f) x^6\right )}{a+b x^3} \, dx}{14 b}\\ &=\frac {f x^{14}}{14 b}+\frac {\int \left (-\frac {14 a \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x}{b^4}+\frac {14 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^4}{b^3}+\frac {14 \left (b^2 d-a b e+a^2 f\right ) x^7}{b^2}+\frac {14 (b e-a f) x^{10}}{b}-\frac {14 \left (-a^2 b^3 c+a^3 b^2 d-a^4 b e+a^5 f\right ) x}{b^4 \left (a+b x^3\right )}\right ) \, dx}{14 b}\\ &=-\frac {a \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{2 b^5}+\frac {\left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^5}{5 b^4}+\frac {\left (b^2 d-a b e+a^2 f\right ) x^8}{8 b^3}+\frac {(b e-a f) x^{11}}{11 b^2}+\frac {f x^{14}}{14 b}+\frac {\left (a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right )\right ) \int \frac {x}{a+b x^3} \, dx}{b^5}\\ &=-\frac {a \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{2 b^5}+\frac {\left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^5}{5 b^4}+\frac {\left (b^2 d-a b e+a^2 f\right ) x^8}{8 b^3}+\frac {(b e-a f) x^{11}}{11 b^2}+\frac {f x^{14}}{14 b}-\frac {\left (a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right )\right ) \int \frac {1}{\sqrt [3]{a}+\sqrt [3]{b} x} \, dx}{3 b^{16/3}}+\frac {\left (a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-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}{3 b^{16/3}}\\ &=-\frac {a \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{2 b^5}+\frac {\left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^5}{5 b^4}+\frac {\left (b^2 d-a b e+a^2 f\right ) x^8}{8 b^3}+\frac {(b e-a f) x^{11}}{11 b^2}+\frac {f x^{14}}{14 b}-\frac {a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{3 b^{17/3}}+\frac {\left (a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-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}{6 b^{17/3}}+\frac {\left (a^2 \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right )\right ) \int \frac {1}{a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2} \, dx}{2 b^{16/3}}\\ &=-\frac {a \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{2 b^5}+\frac {\left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^5}{5 b^4}+\frac {\left (b^2 d-a b e+a^2 f\right ) x^8}{8 b^3}+\frac {(b e-a f) x^{11}}{11 b^2}+\frac {f x^{14}}{14 b}-\frac {a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{3 b^{17/3}}+\frac {a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right )}{6 b^{17/3}}+\frac {\left (a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-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 )}{b^{17/3}}\\ &=-\frac {a \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^2}{2 b^5}+\frac {\left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) x^5}{5 b^4}+\frac {\left (b^2 d-a b e+a^2 f\right ) x^8}{8 b^3}+\frac {(b e-a f) x^{11}}{11 b^2}+\frac {f x^{14}}{14 b}-\frac {a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) \tan ^{-1}\left (\frac {\sqrt [3]{a}-2 \sqrt [3]{b} x}{\sqrt {3} \sqrt [3]{a}}\right )}{\sqrt {3} b^{17/3}}-\frac {a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right )}{3 b^{17/3}}+\frac {a^{5/3} \left (b^3 c-a b^2 d+a^2 b e-a^3 f\right ) \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right )}{6 b^{17/3}}\\ \end {align*}
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Mathematica [A] time = 0.11, size = 311, normalized size = 0.98 \[ \frac {x^8 \left (a^2 f-a b e+b^2 d\right )}{8 b^3}+\frac {a x^2 \left (a^3 f-a^2 b e+a b^2 d-b^3 c\right )}{2 b^5}+\frac {x^5 \left (a^3 (-f)+a^2 b e-a b^2 d+b^3 c\right )}{5 b^4}-\frac {a^{5/3} \log \left (a^{2/3}-\sqrt [3]{a} \sqrt [3]{b} x+b^{2/3} x^2\right ) \left (a^3 f-a^2 b e+a b^2 d-b^3 c\right )}{6 b^{17/3}}+\frac {a^{5/3} \log \left (\sqrt [3]{a}+\sqrt [3]{b} x\right ) \left (a^3 f-a^2 b e+a b^2 d-b^3 c\right )}{3 b^{17/3}}+\frac {a^{5/3} \tan ^{-1}\left (\frac {1-\frac {2 \sqrt [3]{b} x}{\sqrt [3]{a}}}{\sqrt {3}}\right ) \left (a^3 f-a^2 b e+a b^2 d-b^3 c\right )}{\sqrt {3} b^{17/3}}+\frac {x^{11} (b e-a f)}{11 b^2}+\frac {f x^{14}}{14 b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 321, normalized size = 1.02 \[ \frac {660 \, b^{4} f x^{14} + 840 \, {\left (b^{4} e - a b^{3} f\right )} x^{11} + 1155 \, {\left (b^{4} d - a b^{3} e + a^{2} b^{2} f\right )} x^{8} + 1848 \, {\left (b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right )} x^{5} - 4620 \, {\left (a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right )} x^{2} + 3080 \, \sqrt {3} {\left (a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right )} \left (\frac {a^{2}}{b^{2}}\right )^{\frac {1}{3}} \arctan \left (\frac {2 \, \sqrt {3} b x \left (\frac {a^{2}}{b^{2}}\right )^{\frac {1}{3}} - \sqrt {3} a}{3 \, a}\right ) + 1540 \, {\left (a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right )} \left (\frac {a^{2}}{b^{2}}\right )^{\frac {1}{3}} \log \left (a x^{2} - b x \left (\frac {a^{2}}{b^{2}}\right )^{\frac {2}{3}} + a \left (\frac {a^{2}}{b^{2}}\right )^{\frac {1}{3}}\right ) - 3080 \, {\left (a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right )} \left (\frac {a^{2}}{b^{2}}\right )^{\frac {1}{3}} \log \left (a x + b \left (\frac {a^{2}}{b^{2}}\right )^{\frac {2}{3}}\right )}{9240 \, b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 441, normalized size = 1.40 \[ -\frac {\sqrt {3} {\left (\left (-a b^{2}\right )^{\frac {2}{3}} a b^{3} c - \left (-a b^{2}\right )^{\frac {2}{3}} a^{2} b^{2} d - \left (-a b^{2}\right )^{\frac {2}{3}} a^{4} f + \left (-a b^{2}\right )^{\frac {2}{3}} a^{3} b e\right )} \arctan \left (\frac {\sqrt {3} {\left (2 \, x + \left (-\frac {a}{b}\right )^{\frac {1}{3}}\right )}}{3 \, \left (-\frac {a}{b}\right )^{\frac {1}{3}}}\right )}{3 \, b^{7}} + \frac {{\left (\left (-a b^{2}\right )^{\frac {2}{3}} a b^{3} c - \left (-a b^{2}\right )^{\frac {2}{3}} a^{2} b^{2} d - \left (-a b^{2}\right )^{\frac {2}{3}} a^{4} f + \left (-a b^{2}\right )^{\frac {2}{3}} a^{3} b e\right )} \log \left (x^{2} + x \left (-\frac {a}{b}\right )^{\frac {1}{3}} + \left (-\frac {a}{b}\right )^{\frac {2}{3}}\right )}{6 \, b^{7}} - \frac {{\left (a^{2} b^{12} c \left (-\frac {a}{b}\right )^{\frac {1}{3}} - a^{3} b^{11} d \left (-\frac {a}{b}\right )^{\frac {1}{3}} - a^{5} b^{9} f \left (-\frac {a}{b}\right )^{\frac {1}{3}} + a^{4} b^{10} \left (-\frac {a}{b}\right )^{\frac {1}{3}} e\right )} \left (-\frac {a}{b}\right )^{\frac {1}{3}} \log \left ({\left | x - \left (-\frac {a}{b}\right )^{\frac {1}{3}} \right |}\right )}{3 \, a b^{14}} + \frac {220 \, b^{13} f x^{14} - 280 \, a b^{12} f x^{11} + 280 \, b^{13} x^{11} e + 385 \, b^{13} d x^{8} + 385 \, a^{2} b^{11} f x^{8} - 385 \, a b^{12} x^{8} e + 616 \, b^{13} c x^{5} - 616 \, a b^{12} d x^{5} - 616 \, a^{3} b^{10} f x^{5} + 616 \, a^{2} b^{11} x^{5} e - 1540 \, a b^{12} c x^{2} + 1540 \, a^{2} b^{11} d x^{2} + 1540 \, a^{4} b^{9} f x^{2} - 1540 \, a^{3} b^{10} x^{2} e}{3080 \, b^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 554, normalized size = 1.75 \[ \frac {f \,x^{14}}{14 b}-\frac {a f \,x^{11}}{11 b^{2}}+\frac {e \,x^{11}}{11 b}+\frac {a^{2} f \,x^{8}}{8 b^{3}}-\frac {a e \,x^{8}}{8 b^{2}}+\frac {d \,x^{8}}{8 b}-\frac {a^{3} f \,x^{5}}{5 b^{4}}+\frac {a^{2} e \,x^{5}}{5 b^{3}}-\frac {a d \,x^{5}}{5 b^{2}}+\frac {c \,x^{5}}{5 b}+\frac {a^{4} f \,x^{2}}{2 b^{5}}-\frac {a^{3} e \,x^{2}}{2 b^{4}}+\frac {a^{2} d \,x^{2}}{2 b^{3}}-\frac {a c \,x^{2}}{2 b^{2}}-\frac {\sqrt {3}\, a^{5} f \arctan \left (\frac {\sqrt {3}\, \left (\frac {2 x}{\left (\frac {a}{b}\right )^{\frac {1}{3}}}-1\right )}{3}\right )}{3 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{6}}+\frac {a^{5} f \ln \left (x +\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{3 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{6}}-\frac {a^{5} f \ln \left (x^{2}-\left (\frac {a}{b}\right )^{\frac {1}{3}} x +\left (\frac {a}{b}\right )^{\frac {2}{3}}\right )}{6 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{6}}+\frac {\sqrt {3}\, a^{4} e \arctan \left (\frac {\sqrt {3}\, \left (\frac {2 x}{\left (\frac {a}{b}\right )^{\frac {1}{3}}}-1\right )}{3}\right )}{3 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{5}}-\frac {a^{4} e \ln \left (x +\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{3 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{5}}+\frac {a^{4} e \ln \left (x^{2}-\left (\frac {a}{b}\right )^{\frac {1}{3}} x +\left (\frac {a}{b}\right )^{\frac {2}{3}}\right )}{6 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{5}}-\frac {\sqrt {3}\, a^{3} d \arctan \left (\frac {\sqrt {3}\, \left (\frac {2 x}{\left (\frac {a}{b}\right )^{\frac {1}{3}}}-1\right )}{3}\right )}{3 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{4}}+\frac {a^{3} d \ln \left (x +\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{3 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{4}}-\frac {a^{3} d \ln \left (x^{2}-\left (\frac {a}{b}\right )^{\frac {1}{3}} x +\left (\frac {a}{b}\right )^{\frac {2}{3}}\right )}{6 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{4}}+\frac {\sqrt {3}\, a^{2} c \arctan \left (\frac {\sqrt {3}\, \left (\frac {2 x}{\left (\frac {a}{b}\right )^{\frac {1}{3}}}-1\right )}{3}\right )}{3 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{3}}-\frac {a^{2} c \ln \left (x +\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{3 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{3}}+\frac {a^{2} c \ln \left (x^{2}-\left (\frac {a}{b}\right )^{\frac {1}{3}} x +\left (\frac {a}{b}\right )^{\frac {2}{3}}\right )}{6 \left (\frac {a}{b}\right )^{\frac {1}{3}} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.95, size = 313, normalized size = 0.99 \[ \frac {\sqrt {3} {\left (a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right )} \arctan \left (\frac {\sqrt {3} {\left (2 \, x - \left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}}{3 \, \left (\frac {a}{b}\right )^{\frac {1}{3}}}\right )}{3 \, b^{6} \left (\frac {a}{b}\right )^{\frac {1}{3}}} + \frac {220 \, b^{4} f x^{14} + 280 \, {\left (b^{4} e - a b^{3} f\right )} x^{11} + 385 \, {\left (b^{4} d - a b^{3} e + a^{2} b^{2} f\right )} x^{8} + 616 \, {\left (b^{4} c - a b^{3} d + a^{2} b^{2} e - a^{3} b f\right )} x^{5} - 1540 \, {\left (a b^{3} c - a^{2} b^{2} d + a^{3} b e - a^{4} f\right )} x^{2}}{3080 \, b^{5}} + \frac {{\left (a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right )} \log \left (x^{2} - x \left (\frac {a}{b}\right )^{\frac {1}{3}} + \left (\frac {a}{b}\right )^{\frac {2}{3}}\right )}{6 \, b^{6} \left (\frac {a}{b}\right )^{\frac {1}{3}}} - \frac {{\left (a^{2} b^{3} c - a^{3} b^{2} d + a^{4} b e - a^{5} f\right )} \log \left (x + \left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{3 \, b^{6} \left (\frac {a}{b}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.16, size = 313, normalized size = 0.99 \[ x^{11}\,\left (\frac {e}{11\,b}-\frac {a\,f}{11\,b^2}\right )+x^8\,\left (\frac {d}{8\,b}-\frac {a\,\left (\frac {e}{b}-\frac {a\,f}{b^2}\right )}{8\,b}\right )+x^5\,\left (\frac {c}{5\,b}-\frac {a\,\left (\frac {d}{b}-\frac {a\,\left (\frac {e}{b}-\frac {a\,f}{b^2}\right )}{b}\right )}{5\,b}\right )+\frac {f\,x^{14}}{14\,b}-\frac {a^{5/3}\,\ln \left (b^{1/3}\,x+a^{1/3}\right )\,\left (-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right )}{3\,b^{17/3}}-\frac {a\,x^2\,\left (\frac {c}{b}-\frac {a\,\left (\frac {d}{b}-\frac {a\,\left (\frac {e}{b}-\frac {a\,f}{b^2}\right )}{b}\right )}{b}\right )}{2\,b}+\frac {a^{5/3}\,\ln \left (2\,b^{1/3}\,x-a^{1/3}+\sqrt {3}\,a^{1/3}\,1{}\mathrm {i}\right )\,\left (\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\left (-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right )}{3\,b^{17/3}}-\frac {a^{5/3}\,\ln \left (a^{1/3}-2\,b^{1/3}\,x+\sqrt {3}\,a^{1/3}\,1{}\mathrm {i}\right )\,\left (-\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\left (-f\,a^3+e\,a^2\,b-d\,a\,b^2+c\,b^3\right )}{3\,b^{17/3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.06, size = 513, normalized size = 1.62 \[ x^{11} \left (- \frac {a f}{11 b^{2}} + \frac {e}{11 b}\right ) + x^{8} \left (\frac {a^{2} f}{8 b^{3}} - \frac {a e}{8 b^{2}} + \frac {d}{8 b}\right ) + x^{5} \left (- \frac {a^{3} f}{5 b^{4}} + \frac {a^{2} e}{5 b^{3}} - \frac {a d}{5 b^{2}} + \frac {c}{5 b}\right ) + x^{2} \left (\frac {a^{4} f}{2 b^{5}} - \frac {a^{3} e}{2 b^{4}} + \frac {a^{2} d}{2 b^{3}} - \frac {a c}{2 b^{2}}\right ) + \operatorname {RootSum} {\left (27 t^{3} b^{17} - a^{14} f^{3} + 3 a^{13} b e f^{2} - 3 a^{12} b^{2} d f^{2} - 3 a^{12} b^{2} e^{2} f + 3 a^{11} b^{3} c f^{2} + 6 a^{11} b^{3} d e f + a^{11} b^{3} e^{3} - 6 a^{10} b^{4} c e f - 3 a^{10} b^{4} d^{2} f - 3 a^{10} b^{4} d e^{2} + 6 a^{9} b^{5} c d f + 3 a^{9} b^{5} c e^{2} + 3 a^{9} b^{5} d^{2} e - 3 a^{8} b^{6} c^{2} f - 6 a^{8} b^{6} c d e - a^{8} b^{6} d^{3} + 3 a^{7} b^{7} c^{2} e + 3 a^{7} b^{7} c d^{2} - 3 a^{6} b^{8} c^{2} d + a^{5} b^{9} c^{3}, \left (t \mapsto t \log {\left (\frac {9 t^{2} b^{11}}{a^{9} f^{2} - 2 a^{8} b e f + 2 a^{7} b^{2} d f + a^{7} b^{2} e^{2} - 2 a^{6} b^{3} c f - 2 a^{6} b^{3} d e + 2 a^{5} b^{4} c e + a^{5} b^{4} d^{2} - 2 a^{4} b^{5} c d + a^{3} b^{6} c^{2}} + x \right )} \right )\right )} + \frac {f x^{14}}{14 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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