Optimal. Leaf size=17 \[ -2-e^{-1+x}+\frac {1}{4 x^3}+x \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 6, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14, 2194} \begin {gather*} \frac {1}{4 x^3}+x-e^{x-1} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {-3+4 x^4-4 e^{-1+x} x^4}{x^4} \, dx\\ &=\frac {1}{4} \int \left (-4 e^{-1+x}+\frac {-3+4 x^4}{x^4}\right ) \, dx\\ &=\frac {1}{4} \int \frac {-3+4 x^4}{x^4} \, dx-\int e^{-1+x} \, dx\\ &=-e^{-1+x}+\frac {1}{4} \int \left (4-\frac {3}{x^4}\right ) \, dx\\ &=-e^{-1+x}+\frac {1}{4 x^3}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.94 \begin {gather*} -e^{-1+x}+\frac {1}{4 x^3}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 21, normalized size = 1.24 \begin {gather*} \frac {4 \, x^{4} - 4 \, x^{3} e^{\left (x - 1\right )} + 1}{4 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 24, normalized size = 1.41 \begin {gather*} \frac {{\left (4 \, x^{4} e - 4 \, x^{3} e^{x} + e\right )} e^{\left (-1\right )}}{4 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 14, normalized size = 0.82
method | result | size |
risch | \(x +\frac {1}{4 x^{3}}-{\mathrm e}^{x -1}\) | \(14\) |
derivativedivides | \(\frac {1}{4 x^{3}}+x -1-{\mathrm e}^{x -1}\) | \(15\) |
default | \(\frac {1}{4 x^{3}}+x -1-{\mathrm e}^{x -1}\) | \(15\) |
norman | \(\frac {\frac {1}{4}+x^{4}-x^{3} {\mathrm e}^{x -1}}{x^{3}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 13, normalized size = 0.76 \begin {gather*} x + \frac {1}{4 \, x^{3}} - e^{\left (x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 13, normalized size = 0.76 \begin {gather*} x-{\mathrm {e}}^{x-1}+\frac {1}{4\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.71 \begin {gather*} x - e^{x - 1} + \frac {1}{4 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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