Optimal. Leaf size=15 \[ -\frac {e^8}{x^3}+x+3 x^4 \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \begin {gather*} 3 x^4-\frac {e^8}{x^3}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {3 e^8}{x^4}+12 x^3\right ) \, dx\\ &=-\frac {e^8}{x^3}+x+3 x^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {e^8}{x^3}+x+3 x^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 17, normalized size = 1.13 \begin {gather*} \frac {3 \, x^{7} + x^{4} - e^{8}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 14, normalized size = 0.93 \begin {gather*} 3 \, x^{4} + x - \frac {e^{8}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 15, normalized size = 1.00
method | result | size |
default | \(3 x^{4}+x -\frac {{\mathrm e}^{8}}{x^{3}}\) | \(15\) |
risch | \(3 x^{4}+x -\frac {{\mathrm e}^{8}}{x^{3}}\) | \(15\) |
norman | \(\frac {3 x^{7}+x^{4}-{\mathrm e}^{8}}{x^{3}}\) | \(20\) |
gosper | \(-\frac {-3 x^{7}-x^{4}+{\mathrm e}^{8}}{x^{3}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 14, normalized size = 0.93 \begin {gather*} 3 \, x^{4} + x - \frac {e^{8}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.05, size = 17, normalized size = 1.13 \begin {gather*} \frac {3\,x^7+x^4-{\mathrm {e}}^8}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.80 \begin {gather*} 3 x^{4} + x - \frac {e^{8}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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