Optimal. Leaf size=27 \[ \frac {1}{2} \left (3-e^x+\frac {x^2}{4}-10 \left (e^{5+x}+x\right )\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 25, normalized size of antiderivative = 0.93, number of steps
used = 4, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 2225}
\begin {gather*} \frac {x^2}{8}-5 x-\frac {e^x}{2}-5 e^{x+5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \left (-20-2 e^x-20 e^{5+x}+x\right ) \, dx\\ &=-5 x+\frac {x^2}{8}-\frac {\int e^x \, dx}{2}-5 \int e^{5+x} \, dx\\ &=-\frac {e^x}{2}-5 e^{5+x}-5 x+\frac {x^2}{8}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 1.00 \begin {gather*} \frac {1}{4} \left (-2 e^x-20 e^{5+x}-20 x+\frac {x^2}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 20, normalized size = 0.74
method | result | size |
norman | \(\left (-5 \,{\mathrm e}^{5}-\frac {1}{2}\right ) {\mathrm e}^{x}-5 x +\frac {x^{2}}{8}\) | \(19\) |
default | \(-5 x +\frac {x^{2}}{8}-\frac {{\mathrm e}^{x}}{2}-5 \,{\mathrm e}^{5+x}\) | \(20\) |
risch | \(-5 x +\frac {x^{2}}{8}-\frac {{\mathrm e}^{x}}{2}-5 \,{\mathrm e}^{5+x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 19, normalized size = 0.70 \begin {gather*} \frac {1}{8} \, x^{2} - 5 \, x - 5 \, e^{\left (x + 5\right )} - \frac {1}{2} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 27, normalized size = 1.00 \begin {gather*} \frac {1}{8} \, {\left ({\left (x^{2} - 40 \, x\right )} e^{5} - 4 \, {\left (10 \, e^{5} + 1\right )} e^{\left (x + 5\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 20, normalized size = 0.74 \begin {gather*} \frac {x^{2}}{8} - 5 x + \frac {\left (- 10 e^{5} - 1\right ) e^{x}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 19, normalized size = 0.70 \begin {gather*} \frac {1}{8} \, x^{2} - 5 \, x - 5 \, e^{\left (x + 5\right )} - \frac {1}{2} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.19, size = 19, normalized size = 0.70 \begin {gather*} \frac {x^2}{8}-{\mathrm {e}}^x\,\left (5\,{\mathrm {e}}^5+\frac {1}{2}\right )-5\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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