Optimal. Leaf size=113 \[ -\frac {a^5 A}{15 x^{15}}-\frac {a^4 (a B+5 A b)}{12 x^{12}}-\frac {5 a^3 b (a B+2 A b)}{9 x^9}-\frac {5 a^2 b^2 (a B+A b)}{3 x^6}+b^4 \log (x) (5 a B+A b)-\frac {5 a b^3 (2 a B+A b)}{3 x^3}+\frac {1}{3} b^5 B x^3 \]
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Rubi [A] time = 0.09, antiderivative size = 113, 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} \begin {gather*} -\frac {5 a^2 b^2 (a B+A b)}{3 x^6}-\frac {a^4 (a B+5 A b)}{12 x^{12}}-\frac {5 a^3 b (a B+2 A b)}{9 x^9}-\frac {a^5 A}{15 x^{15}}-\frac {5 a b^3 (2 a B+A b)}{3 x^3}+b^4 \log (x) (5 a B+A b)+\frac {1}{3} b^5 B x^3 \end {gather*}
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^{16}} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^5 (A+B x)}{x^6} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (b^5 B+\frac {a^5 A}{x^6}+\frac {a^4 (5 A b+a B)}{x^5}+\frac {5 a^3 b (2 A b+a B)}{x^4}+\frac {10 a^2 b^2 (A b+a B)}{x^3}+\frac {5 a b^3 (A b+2 a B)}{x^2}+\frac {b^4 (A b+5 a B)}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^5 A}{15 x^{15}}-\frac {a^4 (5 A b+a B)}{12 x^{12}}-\frac {5 a^3 b (2 A b+a B)}{9 x^9}-\frac {5 a^2 b^2 (A b+a B)}{3 x^6}-\frac {5 a b^3 (A b+2 a B)}{3 x^3}+\frac {1}{3} b^5 B x^3+b^4 (A b+5 a B) \log (x)\\ \end {align*}
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Mathematica [A] time = 0.07, size = 116, normalized size = 1.03 \begin {gather*} b^4 \log (x) (5 a B+A b)-\frac {3 a^5 \left (4 A+5 B x^3\right )+25 a^4 b x^3 \left (3 A+4 B x^3\right )+100 a^3 b^2 x^6 \left (2 A+3 B x^3\right )+300 a^2 b^3 x^9 \left (A+2 B x^3\right )+300 a A b^4 x^{12}-60 b^5 B x^{18}}{180 x^{15}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{16}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.67, size = 123, normalized size = 1.09 \begin {gather*} \frac {60 \, B b^{5} x^{18} + 180 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} \log \relax (x) - 300 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 300 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 100 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 12 \, A a^{5} - 15 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{180 \, x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 145, normalized size = 1.28 \begin {gather*} \frac {1}{3} \, B b^{5} x^{3} + {\left (5 \, B a b^{4} + A b^{5}\right )} \log \left ({\left | x \right |}\right ) - \frac {685 \, B a b^{4} x^{15} + 137 \, A b^{5} x^{15} + 600 \, B a^{2} b^{3} x^{12} + 300 \, A a b^{4} x^{12} + 300 \, B a^{3} b^{2} x^{9} + 300 \, A a^{2} b^{3} x^{9} + 100 \, B a^{4} b x^{6} + 200 \, A a^{3} b^{2} x^{6} + 15 \, B a^{5} x^{3} + 75 \, A a^{4} b x^{3} + 12 \, A a^{5}}{180 \, x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 123, normalized size = 1.09 \begin {gather*} \frac {B \,b^{5} x^{3}}{3}+A \,b^{5} \ln \relax (x )+5 B a \,b^{4} \ln \relax (x )-\frac {5 A a \,b^{4}}{3 x^{3}}-\frac {10 B \,a^{2} b^{3}}{3 x^{3}}-\frac {5 A \,a^{2} b^{3}}{3 x^{6}}-\frac {5 B \,a^{3} b^{2}}{3 x^{6}}-\frac {10 A \,a^{3} b^{2}}{9 x^{9}}-\frac {5 B \,a^{4} b}{9 x^{9}}-\frac {5 A \,a^{4} b}{12 x^{12}}-\frac {B \,a^{5}}{12 x^{12}}-\frac {A \,a^{5}}{15 x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 123, normalized size = 1.09 \begin {gather*} \frac {1}{3} \, B b^{5} x^{3} + \frac {1}{3} \, {\left (5 \, B a b^{4} + A b^{5}\right )} \log \left (x^{3}\right ) - \frac {300 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 300 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 100 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 12 \, A a^{5} + 15 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{180 \, x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 121, normalized size = 1.07 \begin {gather*} \ln \relax (x)\,\left (A\,b^5+5\,B\,a\,b^4\right )-\frac {\frac {A\,a^5}{15}+x^{12}\,\left (\frac {10\,B\,a^2\,b^3}{3}+\frac {5\,A\,a\,b^4}{3}\right )+x^6\,\left (\frac {5\,B\,a^4\,b}{9}+\frac {10\,A\,a^3\,b^2}{9}\right )+x^3\,\left (\frac {B\,a^5}{12}+\frac {5\,A\,b\,a^4}{12}\right )+x^9\,\left (\frac {5\,B\,a^3\,b^2}{3}+\frac {5\,A\,a^2\,b^3}{3}\right )}{x^{15}}+\frac {B\,b^5\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 29.30, size = 129, normalized size = 1.14 \begin {gather*} \frac {B b^{5} x^{3}}{3} + b^{4} \left (A b + 5 B a\right ) \log {\relax (x )} + \frac {- 12 A a^{5} + x^{12} \left (- 300 A a b^{4} - 600 B a^{2} b^{3}\right ) + x^{9} \left (- 300 A a^{2} b^{3} - 300 B a^{3} b^{2}\right ) + x^{6} \left (- 200 A a^{3} b^{2} - 100 B a^{4} b\right ) + x^{3} \left (- 75 A a^{4} b - 15 B a^{5}\right )}{180 x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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