Optimal. Leaf size=18 \[ -5 e^{-x^2}+x+x \left (x+x^2\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 5, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {6688, 14, 2209} \begin {gather*} x^3+x^2-5 e^{-x^2}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2209
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\left (2+10 e^{-x^2}\right ) x+3 x^2\right ) \, dx\\ &=x+x^3+\int \left (2+10 e^{-x^2}\right ) x \, dx\\ &=x+x^3+\int \left (2 x+10 e^{-x^2} x\right ) \, dx\\ &=x+x^2+x^3+10 \int e^{-x^2} x \, dx\\ &=-5 e^{-x^2}+x+x^2+x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 17, normalized size = 0.94 \begin {gather*} -5 e^{-x^2}+x+x^2+x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 22, normalized size = 1.22 \begin {gather*} {\left ({\left (x^{3} + x^{2} + x\right )} e^{\left (x^{2}\right )} - 5\right )} e^{\left (-x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 16, normalized size = 0.89 \begin {gather*} x^{3} + x^{2} + x - 5 \, e^{\left (-x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.94
method | result | size |
default | \(x^{3}+x^{2}+x -5 \,{\mathrm e}^{-x^{2}}\) | \(17\) |
risch | \(x^{3}+x^{2}+x -5 \,{\mathrm e}^{-x^{2}}\) | \(17\) |
norman | \(\left (-5+x^{2} {\mathrm e}^{x^{2}}+x^{3} {\mathrm e}^{x^{2}}+{\mathrm e}^{x^{2}} x \right ) {\mathrm e}^{-x^{2}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 16, normalized size = 0.89 \begin {gather*} x^{3} + x^{2} + x - 5 \, e^{\left (-x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 16, normalized size = 0.89 \begin {gather*} x-5\,{\mathrm {e}}^{-x^2}+x^2+x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.78 \begin {gather*} x^{3} + x^{2} + x - 5 e^{- x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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