Optimal. Leaf size=42 \[ \frac{1}{4} x^4 (a e+b d)+a d x+\frac{1}{7} x^7 (b e+c d)+\frac{1}{10} c e x^{10} \]
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Rubi [A] time = 0.0278242, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {1407} \[ \frac{1}{4} x^4 (a e+b d)+a d x+\frac{1}{7} x^7 (b e+c d)+\frac{1}{10} c e x^{10} \]
Antiderivative was successfully verified.
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Rule 1407
Rubi steps
\begin{align*} \int \left (d+e x^3\right ) \left (a+b x^3+c x^6\right ) \, dx &=\int \left (a d+(b d+a e) x^3+(c d+b e) x^6+c e x^9\right ) \, dx\\ &=a d x+\frac{1}{4} (b d+a e) x^4+\frac{1}{7} (c d+b e) x^7+\frac{1}{10} c e x^{10}\\ \end{align*}
Mathematica [A] time = 0.0085175, size = 42, normalized size = 1. \[ \frac{1}{4} x^4 (a e+b d)+a d x+\frac{1}{7} x^7 (b e+c d)+\frac{1}{10} c e x^{10} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 37, normalized size = 0.9 \begin{align*} adx+{\frac{ \left ( ae+bd \right ){x}^{4}}{4}}+{\frac{ \left ( be+cd \right ){x}^{7}}{7}}+{\frac{ce{x}^{10}}{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05804, size = 49, normalized size = 1.17 \begin{align*} \frac{1}{10} \, c e x^{10} + \frac{1}{7} \,{\left (c d + b e\right )} x^{7} + \frac{1}{4} \,{\left (b d + a e\right )} x^{4} + a d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.12813, size = 107, normalized size = 2.55 \begin{align*} \frac{1}{10} x^{10} e c + \frac{1}{7} x^{7} d c + \frac{1}{7} x^{7} e b + \frac{1}{4} x^{4} d b + \frac{1}{4} x^{4} e a + x d a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062923, size = 39, normalized size = 0.93 \begin{align*} a d x + \frac{c e x^{10}}{10} + x^{7} \left (\frac{b e}{7} + \frac{c d}{7}\right ) + x^{4} \left (\frac{a e}{4} + \frac{b d}{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09884, size = 58, normalized size = 1.38 \begin{align*} \frac{1}{10} \, c x^{10} e + \frac{1}{7} \, c d x^{7} + \frac{1}{7} \, b x^{7} e + \frac{1}{4} \, b d x^{4} + \frac{1}{4} \, a x^{4} e + a d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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