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 = 0.0129807, antiderivative size = 28, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0054895, size = 28, normalized size = 1. \[ \frac{1}{4} x^4 (a B+A b)+a A x+\frac{1}{7} b B x^7 \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 25, normalized size = 0.9 \begin{align*} aAx+{\frac{ \left ( Ab+Ba \right ){x}^{4}}{4}}+{\frac{bB{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.26996, size = 32, normalized size = 1.14 \begin{align*} \frac{1}{7} \, B b x^{7} + \frac{1}{4} \,{\left (B a + A b\right )} x^{4} + A a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.26144, size = 66, normalized size = 2.36 \begin{align*} \frac{1}{7} x^{7} b B + \frac{1}{4} x^{4} a B + \frac{1}{4} x^{4} b A + x a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.057488, size = 26, normalized size = 0.93 \begin{align*} A a x + \frac{B b x^{7}}{7} + x^{4} \left (\frac{A b}{4} + \frac{B a}{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15625, size = 35, normalized size = 1.25 \begin{align*} \frac{1}{7} \, B b x^{7} + \frac{1}{4} \, B a x^{4} + \frac{1}{4} \, A b x^{4} + A a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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