Optimal. Leaf size=50 \[ \frac {1}{7} d x^7 (a d+2 b c)+\frac {1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac {1}{10} b d^2 x^{10} \]
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Rubi [A] time = 0.03, antiderivative size = 50, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {373} \[ \frac {1}{7} d x^7 (a d+2 b c)+\frac {1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac {1}{10} b d^2 x^{10} \]
Antiderivative was successfully verified.
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Rule 373
Rubi steps
\begin {align*} \int \left (a+b x^3\right ) \left (c+d x^3\right )^2 \, dx &=\int \left (a c^2+c (b c+2 a d) x^3+d (2 b c+a d) x^6+b d^2 x^9\right ) \, dx\\ &=a c^2 x+\frac {1}{4} c (b c+2 a d) x^4+\frac {1}{7} d (2 b c+a d) x^7+\frac {1}{10} b d^2 x^{10}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 50, normalized size = 1.00 \[ \frac {1}{7} d x^7 (a d+2 b c)+\frac {1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac {1}{10} b d^2 x^{10} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.36, size = 50, normalized size = 1.00 \[ \frac {1}{10} x^{10} d^{2} b + \frac {2}{7} x^{7} d c b + \frac {1}{7} x^{7} d^{2} a + \frac {1}{4} x^{4} c^{2} b + \frac {1}{2} x^{4} d c a + x c^{2} a \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 50, normalized size = 1.00 \[ \frac {1}{10} \, b d^{2} x^{10} + \frac {2}{7} \, b c d x^{7} + \frac {1}{7} \, a d^{2} x^{7} + \frac {1}{4} \, b c^{2} x^{4} + \frac {1}{2} \, a c d x^{4} + a c^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 49, normalized size = 0.98 \[ \frac {b \,d^{2} x^{10}}{10}+\frac {\left (a \,d^{2}+2 b c d \right ) x^{7}}{7}+a \,c^{2} x +\frac {\left (2 a c d +b \,c^{2}\right ) x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 48, normalized size = 0.96 \[ \frac {1}{10} \, b d^{2} x^{10} + \frac {1}{7} \, {\left (2 \, b c d + a d^{2}\right )} x^{7} + \frac {1}{4} \, {\left (b c^{2} + 2 \, a c d\right )} x^{4} + a c^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 48, normalized size = 0.96 \[ x^4\,\left (\frac {b\,c^2}{4}+\frac {a\,d\,c}{2}\right )+x^7\,\left (\frac {a\,d^2}{7}+\frac {2\,b\,c\,d}{7}\right )+\frac {b\,d^2\,x^{10}}{10}+a\,c^2\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 51, normalized size = 1.02 \[ a c^{2} x + \frac {b d^{2} x^{10}}{10} + x^{7} \left (\frac {a d^{2}}{7} + \frac {2 b c d}{7}\right ) + x^{4} \left (\frac {a c d}{2} + \frac {b c^{2}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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