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 = 0.0426525, antiderivative size = 70, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0125842, size = 70, normalized size = 1. \[ \frac{1}{4} c^2 x^4 (3 a d+b c)+\frac{1}{10} d^2 x^{10} (a d+3 b c)+\frac{3}{7} c d x^7 (a d+b c)+a c^3 x+\frac{1}{13} b d^3 x^{13} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 73, normalized size = 1. \begin{align*}{\frac{b{d}^{3}{x}^{13}}{13}}+{\frac{ \left ( a{d}^{3}+3\,bc{d}^{2} \right ){x}^{10}}{10}}+{\frac{ \left ( 3\,ac{d}^{2}+3\,b{c}^{2}d \right ){x}^{7}}{7}}+{\frac{ \left ( 3\,a{c}^{2}d+b{c}^{3} \right ){x}^{4}}{4}}+a{c}^{3}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955029, size = 95, normalized size = 1.36 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.34321, size = 182, normalized size = 2.6 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.077301, size = 80, normalized size = 1.14 \begin{align*} 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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10375, size = 100, normalized size = 1.43 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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