Optimal. Leaf size=114 \[ -\frac {a^5 A}{6 x^6}-\frac {a^4 (a B+5 A b)}{3 x^3}+5 a^3 b \log (x) (a B+2 A b)+\frac {10}{3} a^2 b^2 x^3 (a B+A b)+\frac {1}{9} b^4 x^9 (5 a B+A b)+\frac {5}{6} a b^3 x^6 (2 a B+A b)+\frac {1}{12} b^5 B x^{12} \]
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Rubi [A] time = 0.11, antiderivative size = 114, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {446, 76} \[ \frac {10}{3} a^2 b^2 x^3 (a B+A b)-\frac {a^4 (a B+5 A b)}{3 x^3}+5 a^3 b \log (x) (a B+2 A b)-\frac {a^5 A}{6 x^6}+\frac {1}{9} b^4 x^9 (5 a B+A b)+\frac {5}{6} a b^3 x^6 (2 a B+A b)+\frac {1}{12} b^5 B x^{12} \]
Antiderivative was successfully verified.
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Rule 76
Rule 446
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^7} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^5 (A+B x)}{x^3} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (10 a^2 b^2 (A b+a B)+\frac {a^5 A}{x^3}+\frac {a^4 (5 A b+a B)}{x^2}+\frac {5 a^3 b (2 A b+a B)}{x}+5 a b^3 (A b+2 a B) x+b^4 (A b+5 a B) x^2+b^5 B x^3\right ) \, dx,x,x^3\right )\\ &=-\frac {a^5 A}{6 x^6}-\frac {a^4 (5 A b+a B)}{3 x^3}+\frac {10}{3} a^2 b^2 (A b+a B) x^3+\frac {5}{6} a b^3 (A b+2 a B) x^6+\frac {1}{9} b^4 (A b+5 a B) x^9+\frac {1}{12} b^5 B x^{12}+5 a^3 b (2 A b+a B) \log (x)\\ \end {align*}
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Mathematica [A] time = 0.06, size = 106, normalized size = 0.93 \[ \frac {1}{36} \left (-\frac {6 a^5 A}{x^6}-\frac {12 a^4 (a B+5 A b)}{x^3}+180 a^3 b \log (x) (a B+2 A b)+120 a^2 b^2 x^3 (a B+A b)+4 b^4 x^9 (5 a B+A b)+30 a b^3 x^6 (2 a B+A b)+3 b^5 B x^{12}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.13, size = 123, normalized size = 1.08 \[ \frac {3 \, B b^{5} x^{18} + 4 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 30 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 120 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 180 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} \log \relax (x) - 6 \, A a^{5} - 12 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{36 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 148, normalized size = 1.30 \[ \frac {1}{12} \, B b^{5} x^{12} + \frac {5}{9} \, B a b^{4} x^{9} + \frac {1}{9} \, A b^{5} x^{9} + \frac {5}{3} \, B a^{2} b^{3} x^{6} + \frac {5}{6} \, A a b^{4} x^{6} + \frac {10}{3} \, B a^{3} b^{2} x^{3} + \frac {10}{3} \, A a^{2} b^{3} x^{3} + 5 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} \log \left ({\left | x \right |}\right ) - \frac {15 \, B a^{4} b x^{6} + 30 \, A a^{3} b^{2} x^{6} + 2 \, B a^{5} x^{3} + 10 \, A a^{4} b x^{3} + A a^{5}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 124, normalized size = 1.09 \[ \frac {B \,b^{5} x^{12}}{12}+\frac {A \,b^{5} x^{9}}{9}+\frac {5 B a \,b^{4} x^{9}}{9}+\frac {5 A a \,b^{4} x^{6}}{6}+\frac {5 B \,a^{2} b^{3} x^{6}}{3}+\frac {10 A \,a^{2} b^{3} x^{3}}{3}+\frac {10 B \,a^{3} b^{2} x^{3}}{3}+10 A \,a^{3} b^{2} \ln \relax (x )+5 B \,a^{4} b \ln \relax (x )-\frac {5 A \,a^{4} b}{3 x^{3}}-\frac {B \,a^{5}}{3 x^{3}}-\frac {A \,a^{5}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 122, normalized size = 1.07 \[ \frac {1}{12} \, B b^{5} x^{12} + \frac {1}{9} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{9} + \frac {5}{6} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{6} + \frac {10}{3} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + \frac {5}{3} \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} \log \left (x^{3}\right ) - \frac {A a^{5} + 2 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 113, normalized size = 0.99 \[ \ln \relax (x)\,\left (5\,B\,a^4\,b+10\,A\,a^3\,b^2\right )-\frac {\frac {A\,a^5}{6}+x^3\,\left (\frac {B\,a^5}{3}+\frac {5\,A\,b\,a^4}{3}\right )}{x^6}+x^9\,\left (\frac {A\,b^5}{9}+\frac {5\,B\,a\,b^4}{9}\right )+\frac {B\,b^5\,x^{12}}{12}+\frac {10\,a^2\,b^2\,x^3\,\left (A\,b+B\,a\right )}{3}+\frac {5\,a\,b^3\,x^6\,\left (A\,b+2\,B\,a\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.94, size = 131, normalized size = 1.15 \[ \frac {B b^{5} x^{12}}{12} + 5 a^{3} b \left (2 A b + B a\right ) \log {\relax (x )} + x^{9} \left (\frac {A b^{5}}{9} + \frac {5 B a b^{4}}{9}\right ) + x^{6} \left (\frac {5 A a b^{4}}{6} + \frac {5 B a^{2} b^{3}}{3}\right ) + x^{3} \left (\frac {10 A a^{2} b^{3}}{3} + \frac {10 B a^{3} b^{2}}{3}\right ) + \frac {- A a^{5} + x^{3} \left (- 10 A a^{4} b - 2 B a^{5}\right )}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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