Optimal. Leaf size=20 \[ 1-e^x+\frac {16}{x^2}+x+\frac {x \log (2)}{e} \]
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Rubi [A]
time = 0.03, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 6, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {12, 14, 2225}
\begin {gather*} \frac {16}{x^2}-e^x+\frac {x (e+\log (2))}{e} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-e^{1+x} x^3+e \left (-32+x^3\right )+x^3 \log (2)}{x^3} \, dx}{e}\\ &=\frac {\int \left (-e^{1+x}+\frac {-32 e+x^3 (e+\log (2))}{x^3}\right ) \, dx}{e}\\ &=-\frac {\int e^{1+x} \, dx}{e}+\frac {\int \frac {-32 e+x^3 (e+\log (2))}{x^3} \, dx}{e}\\ &=-e^x+\frac {\int \left (-\frac {32 e}{x^3}+e \left (1+\frac {\log (2)}{e}\right )\right ) \, dx}{e}\\ &=-e^x+\frac {16}{x^2}+\frac {x (e+\log (2))}{e}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 0.95 \begin {gather*} -e^x+\frac {16}{x^2}+x+\frac {x \log (2)}{e} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.62, size = 28, normalized size = 1.40
method | result | size |
risch | \({\mathrm e}^{-1} x \,{\mathrm e}+{\mathrm e}^{-1} x \ln \left (2\right )+\frac {16}{x^{2}}-{\mathrm e}^{x}\) | \(23\) |
norman | \(\frac {16+\left ({\mathrm e}+\ln \left (2\right )\right ) {\mathrm e}^{-1} x^{3}-{\mathrm e}^{x} x^{2}}{x^{2}}\) | \(27\) |
default | \({\mathrm e}^{-1} \left (\frac {16 \,{\mathrm e}}{x^{2}}-{\mathrm e} \,{\mathrm e}^{x}+x \,{\mathrm e}+x \ln \left (2\right )\right )\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 25, normalized size = 1.25 \begin {gather*} {\left (x e + x \log \left (2\right ) + \frac {16 \, e}{x^{2}} - e^{\left (x + 1\right )}\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 30, normalized size = 1.50 \begin {gather*} \frac {{\left (x^{3} \log \left (2\right ) - x^{2} e^{\left (x + 1\right )} + {\left (x^{3} + 16\right )} e\right )} e^{\left (-1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 1.10 \begin {gather*} \frac {x \left (\log {\left (2 \right )} + e\right ) + \frac {16 e}{x^{2}}}{e} - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 32, normalized size = 1.60 \begin {gather*} \frac {{\left (x^{3} e + x^{3} \log \left (2\right ) - x^{2} e^{\left (x + 1\right )} + 16 \, e\right )} e^{\left (-1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 19, normalized size = 0.95 \begin {gather*} \frac {16}{x^2}-{\mathrm {e}}^x+x\,{\mathrm {e}}^{-1}\,\left (\mathrm {e}+\ln \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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