Optimal. Leaf size=15 \[ -x+\frac {4 x \left (\frac {3}{2}+x\right )}{e^3} \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.20, number of steps
used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12}
\begin {gather*} \frac {(4 x+3)^2}{4 e^3}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (-e^5+e^2 (6+8 x)\right ) \, dx}{e^5}\\ &=-x+\frac {(3+4 x)^2}{4 e^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 1.27 \begin {gather*} \frac {6 x-e^3 x+4 x^2}{e^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 24, normalized size = 1.60
method | result | size |
gosper | \(-x \left (-4 \,{\mathrm e}^{2} x +{\mathrm e}^{5}-6 \,{\mathrm e}^{2}\right ) {\mathrm e}^{-5}\) | \(20\) |
risch | \(-{\mathrm e}^{-3} {\mathrm e}^{3} x +4 x^{2} {\mathrm e}^{-3}+6 \,{\mathrm e}^{-3} x\) | \(21\) |
default | \({\mathrm e}^{-5} \left (4 x^{2} {\mathrm e}^{2}+6 \,{\mathrm e}^{2} x -x \,{\mathrm e}^{5}\right )\) | \(24\) |
norman | \(4 \,{\mathrm e}^{2} {\mathrm e}^{-5} x^{2}-{\mathrm e}^{-5} \left ({\mathrm e}^{5}-6 \,{\mathrm e}^{2}\right ) x\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 22, normalized size = 1.47 \begin {gather*} -{\left (x e^{5} - 2 \, {\left (2 \, x^{2} + 3 \, x\right )} e^{2}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 17, normalized size = 1.13 \begin {gather*} {\left (4 \, x^{2} - x e^{3} + 6 \, x\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 17, normalized size = 1.13 \begin {gather*} \frac {4 x^{2}}{e^{3}} + \frac {x \left (6 - e^{3}\right )}{e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 22, normalized size = 1.47 \begin {gather*} -{\left (x e^{5} - 2 \, {\left (2 \, x^{2} + 3 \, x\right )} e^{2}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.25, size = 15, normalized size = 1.00 \begin {gather*} \frac {{\mathrm {e}}^{-3}\,{\left (8\,x-{\mathrm {e}}^3+6\right )}^2}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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