Optimal. Leaf size=11 \[ -1-\frac {32}{e^4 x}+x \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 0.91, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14} \begin {gather*} x-\frac {32}{e^4 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 {32+e^4 x^2}{x^2} \, dx}{e^4}\\ &=\frac {\int \left (e^4+\frac {32}{x^2}\right ) \, dx}{e^4}\\ &=-\frac {32}{e^4 x}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 0.91 \begin {gather*} -\frac {32}{e^4 x}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 14, normalized size = 1.27 \begin {gather*} \frac {{\left (x^{2} e^{4} - 32\right )} e^{\left (-4\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 13, normalized size = 1.18 \begin {gather*} {\left (x e^{4} - \frac {32}{x}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 10, normalized size = 0.91
method | result | size |
risch | \(x -\frac {32 \,{\mathrm e}^{-4}}{x}\) | \(10\) |
norman | \(\frac {x^{2}-32 \,{\mathrm e}^{-4}}{x}\) | \(15\) |
default | \({\mathrm e}^{-4} \left (x \,{\mathrm e}^{4}-\frac {32}{x}\right )\) | \(16\) |
gosper | \(\frac {\left (x^{2} {\mathrm e}^{4}-32\right ) {\mathrm e}^{-4}}{x}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 13, normalized size = 1.18 \begin {gather*} {\left (x e^{4} - \frac {32}{x}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.91, size = 9, normalized size = 0.82 \begin {gather*} x-\frac {32\,{\mathrm {e}}^{-4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 10, normalized size = 0.91 \begin {gather*} \frac {x e^{4} - \frac {32}{x}}{e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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