Optimal. Leaf size=25 \[ \frac{a x^2}{2}+\frac{b x^3}{3}+\frac{c x^4}{4} \]
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Rubi [A] time = 0.0075142, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {14} \[ \frac{a x^2}{2}+\frac{b x^3}{3}+\frac{c x^4}{4} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int x \left (a+b x+c x^2\right ) \, dx &=\int \left (a x+b x^2+c x^3\right ) \, dx\\ &=\frac{a x^2}{2}+\frac{b x^3}{3}+\frac{c x^4}{4}\\ \end{align*}
Mathematica [A] time = 0.0012108, size = 25, normalized size = 1. \[ \frac{a x^2}{2}+\frac{b x^3}{3}+\frac{c x^4}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 20, normalized size = 0.8 \begin{align*}{\frac{a{x}^{2}}{2}}+{\frac{b{x}^{3}}{3}}+{\frac{c{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06747, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{4} \, c x^{4} + \frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.15311, size = 47, normalized size = 1.88 \begin{align*} \frac{1}{4} x^{4} c + \frac{1}{3} x^{3} b + \frac{1}{2} x^{2} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058322, size = 19, normalized size = 0.76 \begin{align*} \frac{a x^{2}}{2} + \frac{b x^{3}}{3} + \frac{c x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14749, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{4} \, c x^{4} + \frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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