Optimal. Leaf size=24 \[ -2+\frac {e^4+e^x}{4 x}-x+256 x^3 \]
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Rubi [A] time = 0.04, antiderivative size = 29, normalized size of antiderivative = 1.21, number of steps used = 6, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 14, 2197} \begin {gather*} 256 x^3-x+\frac {e^x}{4 x}+\frac {e^4}{4 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{x^2} \, dx\\ &=\frac {1}{4} \int \left (\frac {e^x (-1+x)}{x^2}+\frac {-e^4-4 x^2+3072 x^4}{x^2}\right ) \, dx\\ &=\frac {1}{4} \int \frac {e^x (-1+x)}{x^2} \, dx+\frac {1}{4} \int \frac {-e^4-4 x^2+3072 x^4}{x^2} \, dx\\ &=\frac {e^x}{4 x}+\frac {1}{4} \int \left (-4-\frac {e^4}{x^2}+3072 x^2\right ) \, dx\\ &=\frac {e^4}{4 x}+\frac {e^x}{4 x}-x+256 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 24, normalized size = 1.00 \begin {gather*} \frac {e^4+e^x-4 x^2+1024 x^4}{4 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 20, normalized size = 0.83 \begin {gather*} \frac {1024 \, x^{4} - 4 \, x^{2} + e^{4} + e^{x}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 20, normalized size = 0.83 \begin {gather*} \frac {1024 \, x^{4} - 4 \, x^{2} + e^{4} + e^{x}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 24, normalized size = 1.00
method | result | size |
default | \(-x +256 x^{3}+\frac {{\mathrm e}^{4}}{4 x}+\frac {{\mathrm e}^{x}}{4 x}\) | \(24\) |
norman | \(\frac {-x^{2}+256 x^{4}+\frac {{\mathrm e}^{4}}{4}+\frac {{\mathrm e}^{x}}{4}}{x}\) | \(24\) |
risch | \(-x +256 x^{3}+\frac {{\mathrm e}^{4}}{4 x}+\frac {{\mathrm e}^{x}}{4 x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.39, size = 27, normalized size = 1.12 \begin {gather*} 256 \, x^{3} - x + \frac {e^{4}}{4 \, x} + \frac {1}{4} \, {\rm Ei}\relax (x) - \frac {1}{4} \, \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 22, normalized size = 0.92 \begin {gather*} \frac {\frac {{\mathrm {e}}^4}{4}+\frac {{\mathrm {e}}^x}{4}}{x}-x+256\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 19, normalized size = 0.79 \begin {gather*} 256 x^{3} - x + \frac {e^{x}}{4 x} + \frac {e^{4}}{4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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