Optimal. Leaf size=28 \[ \frac {1}{4} x^4 (a B+A b)+a A x+\frac {1}{7} b B x^7 \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {373} \[ \frac {1}{4} x^4 (a B+A b)+a A x+\frac {1}{7} b B x^7 \]
Antiderivative was successfully verified.
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Rule 373
Rubi steps
\begin {align*} \int \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A+(A b+a B) x^3+b B x^6\right ) \, dx\\ &=a A x+\frac {1}{4} (A b+a B) x^4+\frac {1}{7} b B x^7\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.00 \[ \frac {1}{4} x^4 (a B+A b)+a A x+\frac {1}{7} b B x^7 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.94, size = 26, normalized size = 0.93 \[ \frac {1}{7} x^{7} b B + \frac {1}{4} x^{4} a B + \frac {1}{4} x^{4} b A + x a A \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 26, normalized size = 0.93 \[ \frac {1}{7} \, B b x^{7} + \frac {1}{4} \, B a x^{4} + \frac {1}{4} \, A b x^{4} + A a x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 25, normalized size = 0.89 \[ \frac {B b \,x^{7}}{7}+\frac {\left (A b +B a \right ) x^{4}}{4}+A a x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 24, normalized size = 0.86 \[ \frac {1}{7} \, B b x^{7} + \frac {1}{4} \, {\left (B a + A b\right )} x^{4} + A a x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 25, normalized size = 0.89 \[ \frac {B\,b\,x^7}{7}+\left (\frac {A\,b}{4}+\frac {B\,a}{4}\right )\,x^4+A\,a\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 26, normalized size = 0.93 \[ A a x + \frac {B b x^{7}}{7} + x^{4} \left (\frac {A b}{4} + \frac {B a}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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