Optimal. Leaf size=56 \[ \frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4 \]
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Rubi [A] time = 0.0164289, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 44, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4 \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3\right ) \, dx &=a c e x+\frac{1}{2} (b c e+a d e+a c f) x^2+\frac{1}{3} (b d e+b c f+a d f) x^3+\frac{1}{4} b d f x^4\\ \end{align*}
Mathematica [A] time = 0.0000704, size = 76, normalized size = 1.36 \[ a c e x+\frac{1}{2} a c f x^2+\frac{1}{2} a d e x^2+\frac{1}{3} a d f x^3+\frac{1}{2} b c e x^2+\frac{1}{3} b c f x^3+\frac{1}{3} b d e x^3+\frac{1}{4} b d f x^4 \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 51, normalized size = 0.9 \begin{align*} acex+{\frac{ \left ( acf+ade+bce \right ){x}^{2}}{2}}+{\frac{ \left ( adf+bcf+bde \right ){x}^{3}}{3}}+{\frac{bdf{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.22255, size = 68, normalized size = 1.21 \begin{align*} \frac{1}{4} \, b d f x^{4} + a c e x + \frac{1}{3} \,{\left (b d e + b c f + a d f\right )} x^{3} + \frac{1}{2} \,{\left (b c e + a d e + a c f\right )} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.08366, size = 163, normalized size = 2.91 \begin{align*} \frac{1}{4} x^{4} f d b + \frac{1}{3} x^{3} e d b + \frac{1}{3} x^{3} f c b + \frac{1}{3} x^{3} f d a + \frac{1}{2} x^{2} e c b + \frac{1}{2} x^{2} e d a + \frac{1}{2} x^{2} f c a + x e c a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067543, size = 63, normalized size = 1.12 \begin{align*} a c e x + \frac{b d f x^{4}}{4} + x^{3} \left (\frac{a d f}{3} + \frac{b c f}{3} + \frac{b d e}{3}\right ) + x^{2} \left (\frac{a c f}{2} + \frac{a d e}{2} + \frac{b c e}{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06873, size = 73, normalized size = 1.3 \begin{align*} \frac{1}{4} \, b d f x^{4} + \frac{1}{3} \,{\left (b c f + a d f + b d e\right )} x^{3} + a c x e + \frac{1}{2} \,{\left (a c f + b c e + a d e\right )} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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