Optimal. Leaf size=112 \[ -\frac {a^5 A}{2 x^2}+a^4 x (a B+5 A b)+\frac {5}{4} a^3 b x^4 (a B+2 A b)+\frac {10}{7} a^2 b^2 x^7 (a B+A b)+\frac {1}{13} b^4 x^{13} (5 a B+A b)+\frac {1}{2} a b^3 x^{10} (2 a B+A b)+\frac {1}{16} b^5 B x^{16} \]
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Rubi [A] time = 0.06, antiderivative size = 112, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {448} \[ \frac {10}{7} a^2 b^2 x^7 (a B+A b)+\frac {5}{4} a^3 b x^4 (a B+2 A b)+a^4 x (a B+5 A b)-\frac {a^5 A}{2 x^2}+\frac {1}{13} b^4 x^{13} (5 a B+A b)+\frac {1}{2} a b^3 x^{10} (2 a B+A b)+\frac {1}{16} b^5 B x^{16} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^3} \, dx &=\int \left (a^4 (5 A b+a B)+\frac {a^5 A}{x^3}+5 a^3 b (2 A b+a B) x^3+10 a^2 b^2 (A b+a B) x^6+5 a b^3 (A b+2 a B) x^9+b^4 (A b+5 a B) x^{12}+b^5 B x^{15}\right ) \, dx\\ &=-\frac {a^5 A}{2 x^2}+a^4 (5 A b+a B) x+\frac {5}{4} a^3 b (2 A b+a B) x^4+\frac {10}{7} a^2 b^2 (A b+a B) x^7+\frac {1}{2} a b^3 (A b+2 a B) x^{10}+\frac {1}{13} b^4 (A b+5 a B) x^{13}+\frac {1}{16} b^5 B x^{16}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 112, normalized size = 1.00 \[ -\frac {a^5 A}{2 x^2}+a^4 x (a B+5 A b)+\frac {5}{4} a^3 b x^4 (a B+2 A b)+\frac {10}{7} a^2 b^2 x^7 (a B+A b)+\frac {1}{13} b^4 x^{13} (5 a B+A b)+\frac {1}{2} a b^3 x^{10} (2 a B+A b)+\frac {1}{16} b^5 B x^{16} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 121, normalized size = 1.08 \[ \frac {91 \, B b^{5} x^{18} + 112 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 728 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 2080 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 1820 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 728 \, A a^{5} + 1456 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{1456 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 119, normalized size = 1.06 \[ \frac {1}{16} \, B b^{5} x^{16} + \frac {5}{13} \, B a b^{4} x^{13} + \frac {1}{13} \, A b^{5} x^{13} + B a^{2} b^{3} x^{10} + \frac {1}{2} \, A a b^{4} x^{10} + \frac {10}{7} \, B a^{3} b^{2} x^{7} + \frac {10}{7} \, A a^{2} b^{3} x^{7} + \frac {5}{4} \, B a^{4} b x^{4} + \frac {5}{2} \, A a^{3} b^{2} x^{4} + B a^{5} x + 5 \, A a^{4} b x - \frac {A a^{5}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 120, normalized size = 1.07 \[ \frac {B \,b^{5} x^{16}}{16}+\frac {A \,b^{5} x^{13}}{13}+\frac {5 B a \,b^{4} x^{13}}{13}+\frac {A a \,b^{4} x^{10}}{2}+B \,a^{2} b^{3} x^{10}+\frac {10 A \,a^{2} b^{3} x^{7}}{7}+\frac {10 B \,a^{3} b^{2} x^{7}}{7}+\frac {5 A \,a^{3} b^{2} x^{4}}{2}+\frac {5 B \,a^{4} b \,x^{4}}{4}+5 A \,a^{4} b x +B \,a^{5} x -\frac {A \,a^{5}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 116, normalized size = 1.04 \[ \frac {1}{16} \, B b^{5} x^{16} + \frac {1}{13} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{13} + \frac {1}{2} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{10} + \frac {10}{7} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{7} + \frac {5}{4} \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} - \frac {A a^{5}}{2 \, x^{2}} + {\left (B a^{5} + 5 \, A a^{4} b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 104, normalized size = 0.93 \[ x\,\left (B\,a^5+5\,A\,b\,a^4\right )+x^{13}\,\left (\frac {A\,b^5}{13}+\frac {5\,B\,a\,b^4}{13}\right )-\frac {A\,a^5}{2\,x^2}+\frac {B\,b^5\,x^{16}}{16}+\frac {10\,a^2\,b^2\,x^7\,\left (A\,b+B\,a\right )}{7}+\frac {5\,a^3\,b\,x^4\,\left (2\,A\,b+B\,a\right )}{4}+\frac {a\,b^3\,x^{10}\,\left (A\,b+2\,B\,a\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 128, normalized size = 1.14 \[ - \frac {A a^{5}}{2 x^{2}} + \frac {B b^{5} x^{16}}{16} + x^{13} \left (\frac {A b^{5}}{13} + \frac {5 B a b^{4}}{13}\right ) + x^{10} \left (\frac {A a b^{4}}{2} + B a^{2} b^{3}\right ) + x^{7} \left (\frac {10 A a^{2} b^{3}}{7} + \frac {10 B a^{3} b^{2}}{7}\right ) + x^{4} \left (\frac {5 A a^{3} b^{2}}{2} + \frac {5 B a^{4} b}{4}\right ) + x \left (5 A a^{4} b + B a^{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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