Optimal. Leaf size=82 \[ \frac {1}{7} x^7 \left (a^2 d^2+4 a b c d+b^2 c^2\right )+a^2 c^2 x+\frac {1}{5} b d x^{10} (a d+b c)+\frac {1}{2} a c x^4 (a d+b c)+\frac {1}{13} b^2 d^2 x^{13} \]
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Rubi [A] time = 0.05, antiderivative size = 82, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {373} \[ \frac {1}{7} x^7 \left (a^2 d^2+4 a b c d+b^2 c^2\right )+a^2 c^2 x+\frac {1}{5} b d x^{10} (a d+b c)+\frac {1}{2} a c x^4 (a d+b c)+\frac {1}{13} b^2 d^2 x^{13} \]
Antiderivative was successfully verified.
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Rule 373
Rubi steps
\begin {align*} \int \left (a+b x^3\right )^2 \left (c+d x^3\right )^2 \, dx &=\int \left (a^2 c^2+2 a c (b c+a d) x^3+\left (b^2 c^2+4 a b c d+a^2 d^2\right ) x^6+2 b d (b c+a d) x^9+b^2 d^2 x^{12}\right ) \, dx\\ &=a^2 c^2 x+\frac {1}{2} a c (b c+a d) x^4+\frac {1}{7} \left (b^2 c^2+4 a b c d+a^2 d^2\right ) x^7+\frac {1}{5} b d (b c+a d) x^{10}+\frac {1}{13} b^2 d^2 x^{13}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 82, normalized size = 1.00 \[ \frac {1}{7} x^7 \left (a^2 d^2+4 a b c d+b^2 c^2\right )+a^2 c^2 x+\frac {1}{5} b d x^{10} (a d+b c)+\frac {1}{2} a c x^4 (a d+b c)+\frac {1}{13} b^2 d^2 x^{13} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.37, size = 91, normalized size = 1.11 \[ \frac {1}{13} x^{13} d^{2} b^{2} + \frac {1}{5} x^{10} d c b^{2} + \frac {1}{5} x^{10} d^{2} b a + \frac {1}{7} x^{7} c^{2} b^{2} + \frac {4}{7} x^{7} d c b a + \frac {1}{7} x^{7} d^{2} a^{2} + \frac {1}{2} x^{4} c^{2} b a + \frac {1}{2} x^{4} d c a^{2} + x c^{2} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 91, normalized size = 1.11 \[ \frac {1}{13} \, b^{2} d^{2} x^{13} + \frac {1}{5} \, b^{2} c d x^{10} + \frac {1}{5} \, a b d^{2} x^{10} + \frac {1}{7} \, b^{2} c^{2} x^{7} + \frac {4}{7} \, a b c d x^{7} + \frac {1}{7} \, a^{2} d^{2} x^{7} + \frac {1}{2} \, a b c^{2} x^{4} + \frac {1}{2} \, a^{2} c d x^{4} + a^{2} c^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 87, normalized size = 1.06 \[ \frac {b^{2} d^{2} x^{13}}{13}+\frac {\left (2 a b \,d^{2}+2 b^{2} c d \right ) x^{10}}{10}+\frac {\left (a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right ) x^{7}}{7}+a^{2} c^{2} x +\frac {\left (2 a^{2} c d +2 a b \,c^{2}\right ) x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.71, size = 82, normalized size = 1.00 \[ \frac {1}{13} \, b^{2} d^{2} x^{13} + \frac {1}{5} \, {\left (b^{2} c d + a b d^{2}\right )} x^{10} + \frac {1}{7} \, {\left (b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right )} x^{7} + a^{2} c^{2} x + \frac {1}{2} \, {\left (a b c^{2} + a^{2} c d\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 75, normalized size = 0.91 \[ x^7\,\left (\frac {a^2\,d^2}{7}+\frac {4\,a\,b\,c\,d}{7}+\frac {b^2\,c^2}{7}\right )+a^2\,c^2\,x+\frac {b^2\,d^2\,x^{13}}{13}+\frac {a\,c\,x^4\,\left (a\,d+b\,c\right )}{2}+\frac {b\,d\,x^{10}\,\left (a\,d+b\,c\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 90, normalized size = 1.10 \[ a^{2} c^{2} x + \frac {b^{2} d^{2} x^{13}}{13} + x^{10} \left (\frac {a b d^{2}}{5} + \frac {b^{2} c d}{5}\right ) + x^{7} \left (\frac {a^{2} d^{2}}{7} + \frac {4 a b c d}{7} + \frac {b^{2} c^{2}}{7}\right ) + x^{4} \left (\frac {a^{2} c d}{2} + \frac {a b c^{2}}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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