Optimal. Leaf size=29 \[ 2+e^{x^2}+x-\log (3)-\log (x)-\log \left (\frac {1}{2} (1-\log (2))\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 11, normalized size of antiderivative = 0.38, number of steps
used = 5, number of rules used = 3, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {14, 45, 2240}
\begin {gather*} e^{x^2}+x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 45
Rule 2240
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-1+x}{x}+2 e^{x^2} x\right ) \, dx\\ &=2 \int e^{x^2} x \, dx+\int \frac {-1+x}{x} \, dx\\ &=e^{x^2}+\int \left (1-\frac {1}{x}\right ) \, dx\\ &=e^{x^2}+x-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.38 \begin {gather*} e^{x^2}+x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 11, normalized size = 0.38
method | result | size |
default | \({\mathrm e}^{x^{2}}-\ln \left (x \right )+x\) | \(11\) |
norman | \({\mathrm e}^{x^{2}}-\ln \left (x \right )+x\) | \(11\) |
risch | \({\mathrm e}^{x^{2}}-\ln \left (x \right )+x\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 10, normalized size = 0.34 \begin {gather*} x + e^{\left (x^{2}\right )} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 10, normalized size = 0.34 \begin {gather*} x + e^{\left (x^{2}\right )} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.28 \begin {gather*} x + e^{x^{2}} - \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 10, normalized size = 0.34 \begin {gather*} x + e^{\left (x^{2}\right )} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 10, normalized size = 0.34 \begin {gather*} x+{\mathrm {e}}^{x^2}-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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