Optimal. Leaf size=17 \[ \frac {b x^2}{2}+\frac {c x^3}{3} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {b x^2}{2}+\frac {c x^3}{3} \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {b x^2}{2}+\frac {c x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (b x+c x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.36, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{3} x^{3} c + \frac {1}{2} x^{2} b \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{3} \, c x^{3} + \frac {1}{2} \, b x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 14, normalized size = 0.82 \begin {gather*} \frac {1}{3} c \,x^{3}+\frac {1}{2} b \,x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{3} \, c x^{3} + \frac {1}{2} \, b x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.76 \begin {gather*} \frac {x^2\,\left (3\,b+2\,c\,x\right )}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 12, normalized size = 0.71 \begin {gather*} \frac {b x^{2}}{2} + \frac {c x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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