Optimal. Leaf size=28 \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4} \]
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Rubi [A] time = 0.0046075, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a+b x+c x^2+d x^3\right ) \, dx &=a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4}\\ \end{align*}
Mathematica [A] time = 0.0000379, size = 28, normalized size = 1. \[ a x+\frac{b x^2}{2}+\frac{c x^3}{3}+\frac{d x^4}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 23, normalized size = 0.8 \begin{align*} ax+{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}}+{\frac{d{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.990462, size = 30, normalized size = 1.07 \begin{align*} \frac{1}{4} \, d x^{4} + \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66902, size = 55, normalized size = 1.96 \begin{align*} \frac{1}{4} x^{4} d + \frac{1}{3} x^{3} c + \frac{1}{2} x^{2} b + x a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.05424, size = 22, normalized size = 0.79 \begin{align*} a x + \frac{b x^{2}}{2} + \frac{c x^{3}}{3} + \frac{d x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05218, size = 30, normalized size = 1.07 \begin{align*} \frac{1}{4} \, d x^{4} + \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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