Optimal. Leaf size=29 \[ \log (x) (a B+A b)-\frac {a A}{3 x^3}+\frac {1}{3} b B x^3 \]
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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*} \log (x) (a B+A b)-\frac {a A}{3 x^3}+\frac {1}{3} b 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 ) \left (A+B x^3\right )}{x^4} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x) (A+B x)}{x^2} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (b B+\frac {a A}{x^2}+\frac {A b+a B}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac {a A}{3 x^3}+\frac {1}{3} b B x^3+(A b+a B) \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.00 \begin {gather*} \log (x) (a B+A b)-\frac {a A}{3 x^3}+\frac {1}{3} b B x^3 \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^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.81, size = 30, normalized size = 1.03 \begin {gather*} \frac {B b x^{6} + 3 \, {\left (B a + A b\right )} x^{3} \log \relax (x) - A a}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 40, normalized size = 1.38 \begin {gather*} \frac {1}{3} \, B b x^{3} + {\left (B a + A b\right )} \log \left ({\left | x \right |}\right ) - \frac {B a x^{3} + A b x^{3} + A a}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 26, normalized size = 0.90 \begin {gather*} \frac {B b \,x^{3}}{3}+A b \ln \relax (x )+B a \ln \relax (x )-\frac {A a}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 28, normalized size = 0.97 \begin {gather*} \frac {1}{3} \, B b x^{3} + \frac {1}{3} \, {\left (B a + A b\right )} \log \left (x^{3}\right ) - \frac {A a}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 25, normalized size = 0.86 \begin {gather*} \ln \relax (x)\,\left (A\,b+B\,a\right )-\frac {A\,a}{3\,x^3}+\frac {B\,b\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 26, normalized size = 0.90 \begin {gather*} - \frac {A a}{3 x^{3}} + \frac {B b x^{3}}{3} + \left (A b + B a\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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