Optimal. Leaf size=17 \[ \frac{b x^2}{2}+\frac{c x^3}{3} \]
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Rubi [A] time = 0.00323, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{b x^2}{2}+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (b x+c x^2\right ) \, dx &=\frac{b x^2}{2}+\frac{c x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0000396, size = 17, normalized size = 1. \[ \frac{b x^2}{2}+\frac{c x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 14, normalized size = 0.8 \begin{align*}{\frac{b{x}^{2}}{2}}+{\frac{c{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15944, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.3568, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{3} x^{3} c + \frac{1}{2} x^{2} b \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.15272, size = 12, normalized size = 0.71 \begin{align*} \frac{b x^{2}}{2} + \frac{c x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.28656, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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