Optimal. Leaf size=19 \[ -10+\frac {5}{e^3}-x+\left (\frac {5}{e}+x\right )^2 \]
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Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12}
\begin {gather*} \frac {1}{4} (1-2 x)^2+\frac {10 x}{e} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int (10+e (-1+2 x)) \, dx}{e}\\ &=\frac {1}{4} (1-2 x)^2+\frac {10 x}{e}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 0.68 \begin {gather*} -x+\frac {10 x}{e}+x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 21, normalized size = 1.11
method | result | size |
risch | \(x^{2}-x +10 \,{\mathrm e}^{-1} x\) | \(13\) |
norman | \(x^{2}-{\mathrm e}^{-1} \left ({\mathrm e}-10\right ) x\) | \(16\) |
gosper | \(x \left (x \,{\mathrm e}-{\mathrm e}+10\right ) {\mathrm e}^{-1}\) | \(17\) |
default | \({\mathrm e}^{-1} \left (x^{2} {\mathrm e}-x \,{\mathrm e}+10 x \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 17, normalized size = 0.89 \begin {gather*} {\left ({\left (x^{2} - x\right )} e + 10 \, x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.29, size = 17, normalized size = 0.89 \begin {gather*} {\left ({\left (x^{2} - x\right )} e + 10 \, x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.63 \begin {gather*} x^{2} + \frac {x \left (10 - e\right )}{e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 0.89 \begin {gather*} {\left ({\left (x^{2} - x\right )} e + 10 \, x\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.27, size = 16, normalized size = 0.84 \begin {gather*} \frac {{\mathrm {e}}^{-2}\,{\left (\mathrm {e}\,\left (2\,x-1\right )+10\right )}^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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