Optimal. Leaf size=10 \[ x^2 \left (-29+e^x+x\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 16, normalized size of antiderivative = 1.60, number of steps
used = 9, number of rules used = 4, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {1607, 2227,
2207, 2225} \begin {gather*} x^3+e^x x^2-29 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} &=-29 x^2+x^3+\int e^x \left (2 x+x^2\right ) \, dx\\ &=-29 x^2+x^3+\int e^x x (2+x) \, dx\\ &=-29 x^2+x^3+\int \left (2 e^x x+e^x x^2\right ) \, dx\\ &=-29 x^2+x^3+2 \int e^x x \, dx+\int e^x x^2 \, dx\\ &=2 e^x x-29 x^2+e^x x^2+x^3-2 \int e^x \, dx-2 \int e^x x \, dx\\ &=-2 e^x-29 x^2+e^x x^2+x^3+2 \int e^x \, dx\\ &=-29 x^2+e^x x^2+x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 10, normalized size = 1.00 \begin {gather*} x^2 \left (-29+e^x+x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.34, size = 16, normalized size = 1.60
method | result | size |
default | \({\mathrm e}^{x} x^{2}-29 x^{2}+x^{3}\) | \(16\) |
norman | \({\mathrm e}^{x} x^{2}-29 x^{2}+x^{3}\) | \(16\) |
risch | \({\mathrm e}^{x} x^{2}-29 x^{2}+x^{3}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 15, normalized size = 1.50 \begin {gather*} x^{3} + x^{2} e^{x} - 29 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 15, normalized size = 1.50 \begin {gather*} x^{3} + x^{2} e^{x} - 29 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 14, normalized size = 1.40 \begin {gather*} x^{3} + x^{2} e^{x} - 29 x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 15, normalized size = 1.50 \begin {gather*} x^{3} + x^{2} e^{x} - 29 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 9, normalized size = 0.90 \begin {gather*} x^2\,\left (x+{\mathrm {e}}^x-29\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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