Optimal. Leaf size=25 \[ \frac{a x^5}{5}+\frac{b x^6}{6}+\frac{c x^7}{7} \]
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Rubi [A] time = 0.0074164, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {14} \[ \frac{a x^5}{5}+\frac{b x^6}{6}+\frac{c x^7}{7} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int x^2 \left (a x^2+b x^3+c x^4\right ) \, dx &=\int \left (a x^4+b x^5+c x^6\right ) \, dx\\ &=\frac{a x^5}{5}+\frac{b x^6}{6}+\frac{c x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0022189, size = 25, normalized size = 1. \[ \frac{a x^5}{5}+\frac{b x^6}{6}+\frac{c x^7}{7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 20, normalized size = 0.8 \begin{align*}{\frac{a{x}^{5}}{5}}+{\frac{b{x}^{6}}{6}}+{\frac{c{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09851, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{7} \, c x^{7} + \frac{1}{6} \, b x^{6} + \frac{1}{5} \, a x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27924, size = 47, normalized size = 1.88 \begin{align*} \frac{1}{7} x^{7} c + \frac{1}{6} x^{6} b + \frac{1}{5} x^{5} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058303, size = 19, normalized size = 0.76 \begin{align*} \frac{a x^{5}}{5} + \frac{b x^{6}}{6} + \frac{c x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09862, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{7} \, c x^{7} + \frac{1}{6} \, b x^{6} + \frac{1}{5} \, a x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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