Optimal. Leaf size=73 \[ \frac{1}{7} x^7 \left (e (a e+2 b d)+c d^2\right )+\frac{1}{4} d x^4 (2 a e+b d)+a d^2 x+\frac{1}{10} e x^{10} (b e+2 c d)+\frac{1}{13} c e^2 x^{13} \]
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Rubi [A] time = 0.0622015, antiderivative size = 73, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {1407} \[ \frac{1}{7} x^7 \left (e (a e+2 b d)+c d^2\right )+\frac{1}{4} d x^4 (2 a e+b d)+a d^2 x+\frac{1}{10} e x^{10} (b e+2 c d)+\frac{1}{13} c e^2 x^{13} \]
Antiderivative was successfully verified.
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Rule 1407
Rubi steps
\begin{align*} \int \left (d+e x^3\right )^2 \left (a+b x^3+c x^6\right ) \, dx &=\int \left (a d^2+d (b d+2 a e) x^3+\left (c d^2+e (2 b d+a e)\right ) x^6+e (2 c d+b e) x^9+c e^2 x^{12}\right ) \, dx\\ &=a d^2 x+\frac{1}{4} d (b d+2 a e) x^4+\frac{1}{7} \left (c d^2+e (2 b d+a e)\right ) x^7+\frac{1}{10} e (2 c d+b e) x^{10}+\frac{1}{13} c e^2 x^{13}\\ \end{align*}
Mathematica [A] time = 0.0218051, size = 73, normalized size = 1. \[ \frac{1}{7} x^7 \left (a e^2+2 b d e+c d^2\right )+\frac{1}{4} d x^4 (2 a e+b d)+a d^2 x+\frac{1}{10} e x^{10} (b e+2 c d)+\frac{1}{13} c e^2 x^{13} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 70, normalized size = 1. \begin{align*}{\frac{c{e}^{2}{x}^{13}}{13}}+{\frac{ \left ( b{e}^{2}+2\,dec \right ){x}^{10}}{10}}+{\frac{ \left ( a{e}^{2}+2\,bde+c{d}^{2} \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,dea+b{d}^{2} \right ){x}^{4}}{4}}+a{d}^{2}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.962235, size = 93, normalized size = 1.27 \begin{align*} \frac{1}{13} \, c e^{2} x^{13} + \frac{1}{10} \,{\left (2 \, c d e + b e^{2}\right )} x^{10} + \frac{1}{7} \,{\left (c d^{2} + 2 \, b d e + a e^{2}\right )} x^{7} + \frac{1}{4} \,{\left (b d^{2} + 2 \, a d e\right )} x^{4} + a d^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.09655, size = 192, normalized size = 2.63 \begin{align*} \frac{1}{13} x^{13} e^{2} c + \frac{1}{5} x^{10} e d c + \frac{1}{10} x^{10} e^{2} b + \frac{1}{7} x^{7} d^{2} c + \frac{2}{7} x^{7} e d b + \frac{1}{7} x^{7} e^{2} a + \frac{1}{4} x^{4} d^{2} b + \frac{1}{2} x^{4} e d a + x d^{2} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.074794, size = 75, normalized size = 1.03 \begin{align*} a d^{2} x + \frac{c e^{2} x^{13}}{13} + x^{10} \left (\frac{b e^{2}}{10} + \frac{c d e}{5}\right ) + x^{7} \left (\frac{a e^{2}}{7} + \frac{2 b d e}{7} + \frac{c d^{2}}{7}\right ) + x^{4} \left (\frac{a d e}{2} + \frac{b d^{2}}{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16215, size = 103, normalized size = 1.41 \begin{align*} \frac{1}{13} \, c x^{13} e^{2} + \frac{1}{5} \, c d x^{10} e + \frac{1}{10} \, b x^{10} e^{2} + \frac{1}{7} \, c d^{2} x^{7} + \frac{2}{7} \, b d x^{7} e + \frac{1}{7} \, a x^{7} e^{2} + \frac{1}{4} \, b d^{2} x^{4} + \frac{1}{2} \, a d x^{4} e + a d^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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