Optimal. Leaf size=18 \[ x+\frac {28 \left (2+x-x^2\right )}{e^5 x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, 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 = {12, 14} \begin {gather*} \frac {56}{e^5 x^2}+x+\frac {28}{e^5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-112-28 x+e^5 x^3}{x^3} \, dx}{e^5}\\ &=\frac {\int \left (e^5-\frac {112}{x^3}-\frac {28}{x^2}\right ) \, dx}{e^5}\\ &=\frac {56}{e^5 x^2}+\frac {28}{e^5 x}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.11 \begin {gather*} \frac {\frac {56}{x^2}+\frac {28}{x}+e^5 x}{e^5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 17, normalized size = 0.94 \begin {gather*} \frac {{\left (x^{3} e^{5} + 28 \, x + 56\right )} e^{\left (-5\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 16, normalized size = 0.89 \begin {gather*} {\left (x e^{5} + \frac {28 \, {\left (x + 2\right )}}{x^{2}}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 14, normalized size = 0.78
method | result | size |
risch | \(x +\frac {{\mathrm e}^{-5} \left (28 x +56\right )}{x^{2}}\) | \(14\) |
gosper | \(\frac {\left (x^{3} {\mathrm e}^{5}+56+28 x \right ) {\mathrm e}^{-5}}{x^{2}}\) | \(20\) |
default | \({\mathrm e}^{-5} \left (x \,{\mathrm e}^{5}+\frac {28}{x}+\frac {56}{x^{2}}\right )\) | \(21\) |
norman | \(\frac {x^{3}+56 \,{\mathrm e}^{-5}+28 x \,{\mathrm e}^{-5}}{x^{2}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 16, normalized size = 0.89 \begin {gather*} {\left (x e^{5} + \frac {28 \, {\left (x + 2\right )}}{x^{2}}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 13, normalized size = 0.72 \begin {gather*} x+\frac {{\mathrm {e}}^{-5}\,\left (28\,x+56\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 15, normalized size = 0.83 \begin {gather*} \frac {x e^{5} + \frac {28 x + 56}{x^{2}}}{e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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