Optimal. Leaf size=70 \[ \frac {1}{4} c^2 x^4 (3 a d+b c)+\frac {1}{10} d^2 x^{10} (a d+3 b c)+\frac {3}{7} c d x^7 (a d+b c)+a c^3 x+\frac {1}{13} b d^3 x^{13} \]
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Rubi [A] time = 0.04, antiderivative size = 70, 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} \[ \frac {1}{4} c^2 x^4 (3 a d+b c)+\frac {1}{10} d^2 x^{10} (a d+3 b c)+\frac {3}{7} c d x^7 (a d+b c)+a c^3 x+\frac {1}{13} b d^3 x^{13} \]
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 )^3 \, dx &=\int \left (a c^3+c^2 (b c+3 a d) x^3+3 c d (b c+a d) x^6+d^2 (3 b c+a d) x^9+b d^3 x^{12}\right ) \, dx\\ &=a c^3 x+\frac {1}{4} c^2 (b c+3 a d) x^4+\frac {3}{7} c d (b c+a d) x^7+\frac {1}{10} d^2 (3 b c+a d) x^{10}+\frac {1}{13} b d^3 x^{13}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 70, normalized size = 1.00 \[ \frac {1}{4} c^2 x^4 (3 a d+b c)+\frac {1}{10} d^2 x^{10} (a d+3 b c)+\frac {3}{7} c d x^7 (a d+b c)+a c^3 x+\frac {1}{13} b d^3 x^{13} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.36, size = 74, normalized size = 1.06 \[ \frac {1}{13} x^{13} d^{3} b + \frac {3}{10} x^{10} d^{2} c b + \frac {1}{10} x^{10} d^{3} a + \frac {3}{7} x^{7} d c^{2} b + \frac {3}{7} x^{7} d^{2} c a + \frac {1}{4} x^{4} c^{3} b + \frac {3}{4} x^{4} d c^{2} a + x c^{3} a \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 74, normalized size = 1.06 \[ \frac {1}{13} \, b d^{3} x^{13} + \frac {3}{10} \, b c d^{2} x^{10} + \frac {1}{10} \, a d^{3} x^{10} + \frac {3}{7} \, b c^{2} d x^{7} + \frac {3}{7} \, a c d^{2} x^{7} + \frac {1}{4} \, b c^{3} x^{4} + \frac {3}{4} \, a c^{2} d x^{4} + a c^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 73, normalized size = 1.04 \[ \frac {b \,d^{3} x^{13}}{13}+\frac {\left (a \,d^{3}+3 b c \,d^{2}\right ) x^{10}}{10}+\frac {\left (3 a c \,d^{2}+3 b \,c^{2} d \right ) x^{7}}{7}+a \,c^{3} x +\frac {\left (3 a \,c^{2} d +b \,c^{3}\right ) x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 70, normalized size = 1.00 \[ \frac {1}{13} \, b d^{3} x^{13} + \frac {1}{10} \, {\left (3 \, b c d^{2} + a d^{3}\right )} x^{10} + \frac {3}{7} \, {\left (b c^{2} d + a c d^{2}\right )} x^{7} + a c^{3} x + \frac {1}{4} \, {\left (b c^{3} + 3 \, a c^{2} d\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 66, normalized size = 0.94 \[ x^4\,\left (\frac {b\,c^3}{4}+\frac {3\,a\,d\,c^2}{4}\right )+x^{10}\,\left (\frac {a\,d^3}{10}+\frac {3\,b\,c\,d^2}{10}\right )+\frac {b\,d^3\,x^{13}}{13}+a\,c^3\,x+\frac {3\,c\,d\,x^7\,\left (a\,d+b\,c\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 80, normalized size = 1.14 \[ a c^{3} x + \frac {b d^{3} x^{13}}{13} + x^{10} \left (\frac {a d^{3}}{10} + \frac {3 b c d^{2}}{10}\right ) + x^{7} \left (\frac {3 a c d^{2}}{7} + \frac {3 b c^{2} d}{7}\right ) + x^{4} \left (\frac {3 a c^{2} d}{4} + \frac {b c^{3}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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