Optimal. Leaf size=29 \[ -\frac {a B+A b}{3 x^3}-\frac {a A}{6 x^6}+b B \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {446, 76} \begin {gather*} -\frac {a B+A b}{3 x^3}-\frac {a A}{6 x^6}+b B \log (x) \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 ) \left (A+B x^3\right )}{x^7} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x) (A+B x)}{x^3} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (\frac {a A}{x^3}+\frac {A b+a B}{x^2}+\frac {b B}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac {a A}{6 x^6}-\frac {A b+a B}{3 x^3}+b B \log (x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 31, normalized size = 1.07 \begin {gather*} \frac {-a B-A b}{3 x^3}-\frac {a A}{6 x^6}+b B \log (x) \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 ) \left (A+B x^3\right )}{x^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.93, size = 31, normalized size = 1.07 \begin {gather*} \frac {6 \, B b x^{6} \log \relax (x) - 2 \, {\left (B a + A b\right )} x^{3} - A a}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 37, normalized size = 1.28 \begin {gather*} B b \log \left ({\left | x \right |}\right ) - \frac {3 \, B b x^{6} + 2 \, B a x^{3} + 2 \, A b x^{3} + A a}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 28, normalized size = 0.97 \begin {gather*} B b \ln \relax (x )-\frac {A b}{3 x^{3}}-\frac {B a}{3 x^{3}}-\frac {A a}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 30, normalized size = 1.03 \begin {gather*} \frac {1}{3} \, B b \log \left (x^{3}\right ) - \frac {2 \, {\left (B a + A b\right )} x^{3} + A a}{6 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 29, normalized size = 1.00 \begin {gather*} B\,b\,\ln \relax (x)-\frac {\left (\frac {A\,b}{3}+\frac {B\,a}{3}\right )\,x^3+\frac {A\,a}{6}}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.54, size = 29, normalized size = 1.00 \begin {gather*} B b \log {\relax (x )} + \frac {- A a + x^{3} \left (- 2 A b - 2 B a\right )}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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