Optimal. Leaf size=19 \[ -e^{4+x}+\frac {1}{16} x \log \left (-\frac {x}{20}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 2225, 2332}
\begin {gather*} \frac {1}{16} x \log \left (-\frac {x}{20}\right )-e^{x+4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rule 2332
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int \left (1-16 e^{4+x}+\log \left (-\frac {x}{20}\right )\right ) \, dx\\ &=\frac {x}{16}+\frac {1}{16} \int \log \left (-\frac {x}{20}\right ) \, dx-\int e^{4+x} \, dx\\ &=-e^{4+x}+\frac {1}{16} x \log \left (-\frac {x}{20}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 20, normalized size = 1.05 \begin {gather*} \frac {1}{16} \left (-16 e^{4+x}+x \log \left (-\frac {x}{20}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 15, normalized size = 0.79
method | result | size |
default | \(\frac {x \ln \left (-\frac {x}{20}\right )}{16}-{\mathrm e}^{4+x}\) | \(15\) |
norman | \(\frac {x \ln \left (-\frac {x}{20}\right )}{16}-{\mathrm e}^{4+x}\) | \(15\) |
risch | \(\frac {x \ln \left (-\frac {x}{20}\right )}{16}-{\mathrm e}^{4+x}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{16} \, x \log \left (-\frac {1}{20} \, x\right ) - e^{\left (x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{16} \, x \log \left (-\frac {1}{20} \, x\right ) - e^{\left (x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 14, normalized size = 0.74 \begin {gather*} \frac {x \log {\left (- \frac {x}{20} \right )}}{16} - e^{x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{16} \, x \log \left (-\frac {1}{20} \, x\right ) - e^{\left (x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.63, size = 14, normalized size = 0.74 \begin {gather*} \frac {x\,\ln \left (-\frac {x}{20}\right )}{16}-{\mathrm {e}}^{x+4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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