Optimal. Leaf size=25 \[ -x-2 e^5 x^2 \left (1+e^x x^3\right )+\log (3)+\log (x) \]
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Rubi [A]
time = 0.11, antiderivative size = 24, normalized size of antiderivative = 0.96, number of steps
used = 17, number of rules used = 4, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {14, 2227,
2207, 2225} \begin {gather*} -2 e^{x+5} x^5-2 e^5 x^2-x+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2207
Rule 2225
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 e^{5+x} x^4 (5+x)+\frac {1-x-4 e^5 x^2}{x}\right ) \, dx\\ &=-\left (2 \int e^{5+x} x^4 (5+x) \, dx\right )+\int \frac {1-x-4 e^5 x^2}{x} \, dx\\ &=-\left (2 \int \left (5 e^{5+x} x^4+e^{5+x} x^5\right ) \, dx\right )+\int \left (-1+\frac {1}{x}-4 e^5 x\right ) \, dx\\ &=-x-2 e^5 x^2+\log (x)-2 \int e^{5+x} x^5 \, dx-10 \int e^{5+x} x^4 \, dx\\ &=-x-2 e^5 x^2-10 e^{5+x} x^4-2 e^{5+x} x^5+\log (x)+10 \int e^{5+x} x^4 \, dx+40 \int e^{5+x} x^3 \, dx\\ &=-x-2 e^5 x^2+40 e^{5+x} x^3-2 e^{5+x} x^5+\log (x)-40 \int e^{5+x} x^3 \, dx-120 \int e^{5+x} x^2 \, dx\\ &=-x-2 e^5 x^2-120 e^{5+x} x^2-2 e^{5+x} x^5+\log (x)+120 \int e^{5+x} x^2 \, dx+240 \int e^{5+x} x \, dx\\ &=-x+240 e^{5+x} x-2 e^5 x^2-2 e^{5+x} x^5+\log (x)-240 \int e^{5+x} \, dx-240 \int e^{5+x} x \, dx\\ &=-240 e^{5+x}-x-2 e^5 x^2-2 e^{5+x} x^5+\log (x)+240 \int e^{5+x} \, dx\\ &=-x-2 e^5 x^2-2 e^{5+x} x^5+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 24, normalized size = 0.96 \begin {gather*} -x \left (1+2 e^5 x+2 e^{5+x} x^4\right )+\log (x) \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. \(88\) vs.
\(2(23)=46\).
time = 0.07, size = 89, normalized size = 3.56
method | result | size |
norman | \(-x -2 x^{2} {\mathrm e}^{5}-2 x^{5} {\mathrm e}^{5} {\mathrm e}^{x}+\ln \left (x \right )\) | \(23\) |
risch | \(-x -2 x^{2} {\mathrm e}^{5}-2 x^{5} {\mathrm e}^{5+x}+\ln \left (x \right )\) | \(23\) |
default | \(\ln \left (x \right )-x -2 x^{2} {\mathrm e}^{5}-10 \,{\mathrm e}^{5} \left ({\mathrm e}^{x} x^{4}-4 \,{\mathrm e}^{x} x^{3}+12 \,{\mathrm e}^{x} x^{2}-24 \,{\mathrm e}^{x} x +24 \,{\mathrm e}^{x}\right )-2 \,{\mathrm e}^{5} \left (x^{5} {\mathrm e}^{x}-5 \,{\mathrm e}^{x} x^{4}+20 \,{\mathrm e}^{x} x^{3}-60 \,{\mathrm e}^{x} x^{2}+120 \,{\mathrm e}^{x} x -120 \,{\mathrm e}^{x}\right )\) | \(89\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 88 vs.
\(2 (23) = 46\).
time = 0.26, size = 88, normalized size = 3.52 \begin {gather*} -2 \, x^{2} e^{5} - 2 \, {\left (x^{5} e^{5} - 5 \, x^{4} e^{5} + 20 \, x^{3} e^{5} - 60 \, x^{2} e^{5} + 120 \, x e^{5} - 120 \, e^{5}\right )} e^{x} - 10 \, {\left (x^{4} e^{5} - 4 \, x^{3} e^{5} + 12 \, x^{2} e^{5} - 24 \, x e^{5} + 24 \, e^{5}\right )} e^{x} - x + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 22, normalized size = 0.88 \begin {gather*} -2 \, x^{5} e^{\left (x + 5\right )} - 2 \, x^{2} e^{5} - x + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 24, normalized size = 0.96 \begin {gather*} - 2 x^{5} e^{5} e^{x} - 2 x^{2} e^{5} - x + \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 22, normalized size = 0.88 \begin {gather*} -2 \, x^{5} e^{\left (x + 5\right )} - 2 \, x^{2} e^{5} - x + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.89, size = 22, normalized size = 0.88 \begin {gather*} \ln \left (x\right )-x-2\,x^5\,{\mathrm {e}}^{x+5}-2\,x^2\,{\mathrm {e}}^5 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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