Optimal. Leaf size=27 \[ \frac {20 \left (4+x+\frac {x+\left (1-e^{3-x}\right ) x}{x}\right )}{x} \]
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Rubi [A] time = 0.04, antiderivative size = 18, normalized size of antiderivative = 0.67, number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {14, 2197} \begin {gather*} \frac {120}{x}-\frac {20 e^{3-x}}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {120}{x^2}+\frac {20 e^{3-x} (1+x)}{x^2}\right ) \, dx\\ &=\frac {120}{x}+20 \int \frac {e^{3-x} (1+x)}{x^2} \, dx\\ &=\frac {120}{x}-\frac {20 e^{3-x}}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 16, normalized size = 0.59 \begin {gather*} \frac {20 \left (6-e^{3-x}\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 13, normalized size = 0.48 \begin {gather*} -\frac {20 \, {\left (e^{\left (-x + 3\right )} - 6\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 13, normalized size = 0.48 \begin {gather*} -\frac {20 \, {\left (e^{\left (-x + 3\right )} - 6\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 15, normalized size = 0.56
method | result | size |
norman | \(\frac {120-20 \,{\mathrm e}^{3-x}}{x}\) | \(15\) |
derivativedivides | \(\frac {120}{x}-\frac {20 \,{\mathrm e}^{3-x}}{x}\) | \(18\) |
default | \(\frac {120}{x}-\frac {20 \,{\mathrm e}^{3-x}}{x}\) | \(18\) |
risch | \(\frac {120}{x}-\frac {20 \,{\mathrm e}^{3-x}}{x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.38, size = 21, normalized size = 0.78 \begin {gather*} 20 \, {\rm Ei}\left (-x\right ) e^{3} - 20 \, e^{3} \Gamma \left (-1, x\right ) + \frac {120}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.00, size = 15, normalized size = 0.56 \begin {gather*} -\frac {20\,{\mathrm {e}}^{3-x}-120}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.37 \begin {gather*} - \frac {20 e^{3 - x}}{x} + \frac {120}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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