Optimal. Leaf size=12 \[ x^2 \left (24+x+e^x x\right ) \]
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Rubi [A]
time = 0.08, antiderivative size = 16, normalized size of antiderivative = 1.33, number of steps
used = 11, number of rules used = 4, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1607, 2227,
2207, 2225} \begin {gather*} e^x x^3+x^3+24 x^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 2207
Rule 2225
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=24 x^2+x^3+\int e^x \left (3 x^2+x^3\right ) \, dx\\ &=24 x^2+x^3+\int e^x x^2 (3+x) \, dx\\ &=24 x^2+x^3+\int \left (3 e^x x^2+e^x x^3\right ) \, dx\\ &=24 x^2+x^3+3 \int e^x x^2 \, dx+\int e^x x^3 \, dx\\ &=24 x^2+3 e^x x^2+x^3+e^x x^3-3 \int e^x x^2 \, dx-6 \int e^x x \, dx\\ &=-6 e^x x+24 x^2+x^3+e^x x^3+6 \int e^x \, dx+6 \int e^x x \, dx\\ &=6 e^x+24 x^2+x^3+e^x x^3-6 \int e^x \, dx\\ &=24 x^2+x^3+e^x x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 12, normalized size = 1.00 \begin {gather*} x^2 \left (24+x+e^x x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 16, normalized size = 1.33
method | result | size |
default | \({\mathrm e}^{x} x^{3}+24 x^{2}+x^{3}\) | \(16\) |
norman | \({\mathrm e}^{x} x^{3}+24 x^{2}+x^{3}\) | \(16\) |
risch | \({\mathrm e}^{x} x^{3}+24 x^{2}+x^{3}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 15, normalized size = 1.25 \begin {gather*} x^{3} e^{x} + x^{3} + 24 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 15, normalized size = 1.25 \begin {gather*} x^{3} e^{x} + x^{3} + 24 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 1.17 \begin {gather*} x^{3} e^{x} + x^{3} + 24 x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 1.25 \begin {gather*} x^{3} e^{x} + x^{3} + 24 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.27, size = 11, normalized size = 0.92 \begin {gather*} x^2\,\left (x+x\,{\mathrm {e}}^x+24\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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