Optimal. Leaf size=26 \[ -6+e^2-x \left (3-e^{3 x}+x-4 (4-x) x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 37, normalized size of antiderivative = 1.42, number of steps used = 3, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2176, 2194} \begin {gather*} -4 x^3+15 x^2-3 x-\frac {e^{3 x}}{3}+\frac {1}{3} e^{3 x} (3 x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-3 x+15 x^2-4 x^3+\int e^{3 x} (1+3 x) \, dx\\ &=-3 x+15 x^2-4 x^3+\frac {1}{3} e^{3 x} (1+3 x)-\int e^{3 x} \, dx\\ &=-\frac {e^{3 x}}{3}-3 x+15 x^2-4 x^3+\frac {1}{3} e^{3 x} (1+3 x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.81 \begin {gather*} -3 x+e^{3 x} x+15 x^2-4 x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 20, normalized size = 0.77 \begin {gather*} -4 \, x^{3} + 15 \, x^{2} + x e^{\left (3 \, x\right )} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 20, normalized size = 0.77 \begin {gather*} -4 \, x^{3} + 15 \, x^{2} + x e^{\left (3 \, x\right )} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 21, normalized size = 0.81
method | result | size |
derivativedivides | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
default | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
norman | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
risch | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 20, normalized size = 0.77 \begin {gather*} -4 \, x^{3} + 15 \, x^{2} + x e^{\left (3 \, x\right )} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 16, normalized size = 0.62 \begin {gather*} x\,\left (15\,x+{\mathrm {e}}^{3\,x}-4\,x^2-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 19, normalized size = 0.73 \begin {gather*} - 4 x^{3} + 15 x^{2} + x e^{3 x} - 3 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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