Optimal. Leaf size=25 \[ 1+\frac {5 e^{25 x^2}}{x}-x-\log (2)-\log (x) \]
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Rubi [A] time = 0.08, antiderivative size = 20, normalized size of antiderivative = 0.80, number of steps used = 5, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {14, 43, 2288} \begin {gather*} \frac {5 e^{25 x^2}}{x}-x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-1-x}{x}+\frac {5 e^{25 x^2} \left (-1+50 x^2\right )}{x^2}\right ) \, dx\\ &=5 \int \frac {e^{25 x^2} \left (-1+50 x^2\right )}{x^2} \, dx+\int \frac {-1-x}{x} \, dx\\ &=\frac {5 e^{25 x^2}}{x}+\int \left (-1-\frac {1}{x}\right ) \, dx\\ &=\frac {5 e^{25 x^2}}{x}-x-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 0.80 \begin {gather*} \frac {5 e^{25 x^2}}{x}-x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 21, normalized size = 0.84 \begin {gather*} -\frac {x^{2} + x \log \relax (x) - 5 \, e^{\left (25 \, x^{2}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 21, normalized size = 0.84 \begin {gather*} -\frac {x^{2} + x \log \relax (x) - 5 \, e^{\left (25 \, x^{2}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 0.80
method | result | size |
default | \(-x -\ln \relax (x )+\frac {5 \,{\mathrm e}^{25 x^{2}}}{x}\) | \(20\) |
risch | \(-x -\ln \relax (x )+\frac {5 \,{\mathrm e}^{25 x^{2}}}{x}\) | \(20\) |
norman | \(\frac {-x^{2}+5 \,{\mathrm e}^{25 x^{2}}}{x}-\ln \relax (x )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.64, size = 36, normalized size = 1.44 \begin {gather*} -25 i \, \sqrt {\pi } \operatorname {erf}\left (5 i \, x\right ) - x + \frac {25 \, \sqrt {-x^{2}} \Gamma \left (-\frac {1}{2}, -25 \, x^{2}\right )}{2 \, x} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 23, normalized size = 0.92 \begin {gather*} \frac {5\,{\mathrm {e}}^{25\,x^2}-x^2}{x}-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.56 \begin {gather*} - x - \log {\relax (x )} + \frac {5 e^{25 x^{2}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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