Optimal. Leaf size=34 \[ \frac{1}{2} x^2 \left (a e^2+c d^2\right )+a d e x+\frac{1}{3} c d e x^3 \]
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Rubi [A] time = 0.0089247, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{1}{2} x^2 \left (a e^2+c d^2\right )+a d e x+\frac{1}{3} c d e x^3 \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a d e+\left (c d^2+a e^2\right ) x+c d e x^2\right ) \, dx &=a d e x+\frac{1}{2} \left (c d^2+a e^2\right ) x^2+\frac{1}{3} c d e x^3\\ \end{align*}
Mathematica [A] time = 0.0000464, size = 38, normalized size = 1.12 \[ a d e x+\frac{1}{2} a e^2 x^2+\frac{1}{2} c d^2 x^2+\frac{1}{3} c d e x^3 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.039, size = 31, normalized size = 0.9 \begin{align*} adex+{\frac{ \left ( a{e}^{2}+c{d}^{2} \right ){x}^{2}}{2}}+{\frac{cde{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0985, size = 41, normalized size = 1.21 \begin{align*} \frac{1}{3} \, c d e x^{3} + a d e x + \frac{1}{2} \,{\left (c d^{2} + a e^{2}\right )} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28492, size = 77, normalized size = 2.26 \begin{align*} \frac{1}{3} x^{3} e d c + \frac{1}{2} x^{2} d^{2} c + \frac{1}{2} x^{2} e^{2} a + x e d a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.188778, size = 32, normalized size = 0.94 \begin{align*} a d e x + \frac{c d e x^{3}}{3} + x^{2} \left (\frac{a e^{2}}{2} + \frac{c d^{2}}{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15327, size = 42, normalized size = 1.24 \begin{align*} \frac{1}{3} \, c d x^{3} e + a d x e + \frac{1}{2} \,{\left (c d^{2} + a e^{2}\right )} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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