Optimal. Leaf size=22 \[ -12-e^{1+x}-\frac {1}{x}-x+5 x^5 \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps
used = 5, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14, 2225}
\begin {gather*} 5 x^5-x-e^{x+1}-\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^{1+x}+\frac {1-x^2+25 x^6}{x^2}\right ) \, dx\\ &=-\int e^{1+x} \, dx+\int \frac {1-x^2+25 x^6}{x^2} \, dx\\ &=-e^{1+x}+\int \left (-1+\frac {1}{x^2}+25 x^4\right ) \, dx\\ &=-e^{1+x}-\frac {1}{x}-x+5 x^5\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 0.95 \begin {gather*} -e^{1+x}-\frac {1}{x}-x+5 x^5 \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(44\) vs.
\(2(21)=42\).
time = 1.17, size = 45, normalized size = 2.05
method | result | size |
risch | \(5 x^{5}-x -\frac {1}{x}-{\mathrm e}^{x +1}\) | \(21\) |
norman | \(\frac {-1-x^{2}+5 x^{6}-x \,{\mathrm e}^{x +1}}{x}\) | \(24\) |
derivativedivides | \(-\frac {1}{x}+24 x +24-50 \left (x +1\right )^{2}+50 \left (x +1\right )^{3}-25 \left (x +1\right )^{4}+5 \left (x +1\right )^{5}-{\mathrm e}^{x +1}\) | \(45\) |
default | \(-\frac {1}{x}+24 x +24-50 \left (x +1\right )^{2}+50 \left (x +1\right )^{3}-25 \left (x +1\right )^{4}+5 \left (x +1\right )^{5}-{\mathrm e}^{x +1}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 20, normalized size = 0.91 \begin {gather*} 5 \, x^{5} - x - \frac {1}{x} - e^{\left (x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 23, normalized size = 1.05 \begin {gather*} \frac {5 \, x^{6} - x^{2} - x e^{\left (x + 1\right )} - 1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 0.64 \begin {gather*} 5 x^{5} - x - e^{x + 1} - \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 23, normalized size = 1.05 \begin {gather*} \frac {5 \, x^{6} - x^{2} - x e^{\left (x + 1\right )} - 1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.12, size = 20, normalized size = 0.91 \begin {gather*} 5\,x^5-{\mathrm {e}}^{x+1}-\frac {1}{x}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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