Optimal. Leaf size=45 \[ \frac{x^{m+4} (a B+A b)}{m+4}+\frac{a A x^{m+1}}{m+1}+\frac{b B x^{m+7}}{m+7} \]
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Rubi [A] time = 0.0206881, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {448} \[ \frac{x^{m+4} (a B+A b)}{m+4}+\frac{a A x^{m+1}}{m+1}+\frac{b B x^{m+7}}{m+7} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int x^m \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A x^m+(A b+a B) x^{3+m}+b B x^{6+m}\right ) \, dx\\ &=\frac{a A x^{1+m}}{1+m}+\frac{(A b+a B) x^{4+m}}{4+m}+\frac{b B x^{7+m}}{7+m}\\ \end{align*}
Mathematica [A] time = 0.0293848, size = 42, normalized size = 0.93 \[ x^{m+1} \left (\frac{x^3 (a B+A b)}{m+4}+\frac{a A}{m+1}+\frac{b B x^6}{m+7}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.004, size = 110, normalized size = 2.4 \begin{align*}{\frac{{x}^{1+m} \left ( Bb{m}^{2}{x}^{6}+5\,Bbm{x}^{6}+4\,bB{x}^{6}+Ab{m}^{2}{x}^{3}+Ba{m}^{2}{x}^{3}+8\,Abm{x}^{3}+8\,Bam{x}^{3}+7\,A{x}^{3}b+7\,B{x}^{3}a+Aa{m}^{2}+11\,Aam+28\,Aa \right ) }{ \left ( 7+m \right ) \left ( 4+m \right ) \left ( 1+m \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.52469, size = 213, normalized size = 4.73 \begin{align*} \frac{{\left ({\left (B b m^{2} + 5 \, B b m + 4 \, B b\right )} x^{7} +{\left ({\left (B a + A b\right )} m^{2} + 7 \, B a + 7 \, A b + 8 \,{\left (B a + A b\right )} m\right )} x^{4} +{\left (A a m^{2} + 11 \, A a m + 28 \, A a\right )} x\right )} x^{m}}{m^{3} + 12 \, m^{2} + 39 \, m + 28} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.46232, size = 410, normalized size = 9.11 \begin{align*} \begin{cases} - \frac{A a}{6 x^{6}} - \frac{A b}{3 x^{3}} - \frac{B a}{3 x^{3}} + B b \log{\left (x \right )} & \text{for}\: m = -7 \\- \frac{A a}{3 x^{3}} + A b \log{\left (x \right )} + B a \log{\left (x \right )} + \frac{B b x^{3}}{3} & \text{for}\: m = -4 \\A a \log{\left (x \right )} + \frac{A b x^{3}}{3} + \frac{B a x^{3}}{3} + \frac{B b x^{6}}{6} & \text{for}\: m = -1 \\\frac{A a m^{2} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{11 A a m x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{28 A a x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{A b m^{2} x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{8 A b m x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{7 A b x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{B a m^{2} x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{8 B a m x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{7 B a x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{B b m^{2} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{5 B b m x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{4 B b x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.12567, size = 193, normalized size = 4.29 \begin{align*} \frac{B b m^{2} x^{7} x^{m} + 5 \, B b m x^{7} x^{m} + 4 \, B b x^{7} x^{m} + B a m^{2} x^{4} x^{m} + A b m^{2} x^{4} x^{m} + 8 \, B a m x^{4} x^{m} + 8 \, A b m x^{4} x^{m} + 7 \, B a x^{4} x^{m} + 7 \, A b x^{4} x^{m} + A a m^{2} x x^{m} + 11 \, A a m x x^{m} + 28 \, A a x x^{m}}{m^{3} + 12 \, m^{2} + 39 \, m + 28} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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