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 = 0.0284518, antiderivative size = 50, 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} \[ \frac{1}{7} d x^7 (a d+2 b c)+\frac{1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac{1}{10} b d^2 x^{10} \]
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*}
Mathematica [A] time = 0.0081618, size = 50, normalized size = 1. \[ \frac{1}{7} d x^7 (a d+2 b c)+\frac{1}{4} c x^4 (2 a d+b c)+a c^2 x+\frac{1}{10} b d^2 x^{10} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 49, normalized size = 1. \begin{align*}{\frac{b{d}^{2}{x}^{10}}{10}}+{\frac{ \left ( a{d}^{2}+2\,bcd \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,acd+b{c}^{2} \right ){x}^{4}}{4}}+a{c}^{2}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.940585, size = 65, normalized size = 1.3 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28691, size = 123, normalized size = 2.46 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.101341, size = 51, normalized size = 1.02 \begin{align*} 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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08964, size = 68, normalized size = 1.36 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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