Optimal. Leaf size=18 \[ -1+e^{20 x}-\frac {e^4}{x}+2 x \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 5, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {14, 2194} \begin {gather*} 2 x+e^{20 x}-\frac {e^4}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (20 e^{20 x}+\frac {e^4+2 x^2}{x^2}\right ) \, dx\\ &=20 \int e^{20 x} \, dx+\int \frac {e^4+2 x^2}{x^2} \, dx\\ &=e^{20 x}+\int \left (2+\frac {e^4}{x^2}\right ) \, dx\\ &=e^{20 x}-\frac {e^4}{x}+2 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.94 \begin {gather*} e^{20 x}-\frac {e^4}{x}+2 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.38, size = 20, normalized size = 1.11 \begin {gather*} \frac {2 \, x^{2} + x e^{\left (20 \, x\right )} - e^{4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 20, normalized size = 1.11 \begin {gather*} \frac {2 \, x^{2} + x e^{\left (20 \, x\right )} - e^{4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 0.89
method | result | size |
derivativedivides | \(2 x -\frac {{\mathrm e}^{4}}{x}+{\mathrm e}^{20 x}\) | \(16\) |
default | \(2 x -\frac {{\mathrm e}^{4}}{x}+{\mathrm e}^{20 x}\) | \(16\) |
risch | \(2 x -\frac {{\mathrm e}^{4}}{x}+{\mathrm e}^{20 x}\) | \(16\) |
norman | \(\frac {x \,{\mathrm e}^{20 x}+2 x^{2}-{\mathrm e}^{4}}{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 15, normalized size = 0.83 \begin {gather*} 2 \, x - \frac {e^{4}}{x} + e^{\left (20 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.57, size = 15, normalized size = 0.83 \begin {gather*} 2\,x+{\mathrm {e}}^{20\,x}-\frac {{\mathrm {e}}^4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 12, normalized size = 0.67 \begin {gather*} 2 x + e^{20 x} - \frac {e^{4}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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