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 = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \[ \frac {a x^2}{2}+\frac {b x^3}{3}+\frac {c x^4}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 19, normalized size = 0.76 \[ \frac {1}{4} x^{4} c + \frac {1}{3} x^{3} b + \frac {1}{2} x^{2} a \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 19, normalized size = 0.76 \[ \frac {1}{4} \, c x^{4} + \frac {1}{3} \, b x^{3} + \frac {1}{2} \, a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 20, normalized size = 0.80 \[ \frac {1}{4} c \,x^{4}+\frac {1}{3} b \,x^{3}+\frac {1}{2} a \,x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 19, normalized size = 0.76 \[ \frac {1}{4} \, c x^{4} + \frac {1}{3} \, b x^{3} + \frac {1}{2} \, a x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 19, normalized size = 0.76 \[ \frac {x^2\,\left (3\,c\,x^2+4\,b\,x+6\,a\right )}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 19, normalized size = 0.76 \[ \frac {a x^{2}}{2} + \frac {b x^{3}}{3} + \frac {c x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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