Optimal. Leaf size=25 \[ -2-x^2+e^5 x^3-\log (4-\log (8+x)) \]
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Rubi [A] time = 0.34, antiderivative size = 24, normalized size of antiderivative = 0.96, number of steps used = 8, number of rules used = 6, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {6741, 6742, 43, 2390, 2302, 29} \begin {gather*} e^5 x^3-x^2-\log (4-\log (x+8)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 43
Rule 2302
Rule 2390
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1-64 x-8 x^2-e^5 \left (-96 x^2-12 x^3\right )-\left (-16 x-2 x^2+e^5 \left (24 x^2+3 x^3\right )\right ) \log (8+x)}{(8+x) (4-\log (8+x))} \, dx\\ &=\int \left (x \left (-2+3 e^5 x\right )-\frac {1}{(8+x) (-4+\log (8+x))}\right ) \, dx\\ &=\int x \left (-2+3 e^5 x\right ) \, dx-\int \frac {1}{(8+x) (-4+\log (8+x))} \, dx\\ &=\int \left (-2 x+3 e^5 x^2\right ) \, dx-\operatorname {Subst}\left (\int \frac {1}{x (-4+\log (x))} \, dx,x,8+x\right )\\ &=-x^2+e^5 x^3-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,-4+\log (8+x)\right )\\ &=-x^2+e^5 x^3-\log (4-\log (8+x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 27, normalized size = 1.08 \begin {gather*} 64-x^2+e^5 \left (512+x^3\right )-\log (4-\log (8+x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 21, normalized size = 0.84 \begin {gather*} x^{3} e^{5} - x^{2} - \log \left (\log \left (x + 8\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 21, normalized size = 0.84 \begin {gather*} x^{3} e^{5} - x^{2} - \log \left (\log \left (x + 8\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 22, normalized size = 0.88
method | result | size |
norman | \(x^{3} {\mathrm e}^{5}-x^{2}-\ln \left (\ln \left (x +8\right )-4\right )\) | \(22\) |
risch | \(x^{3} {\mathrm e}^{5}-x^{2}-\ln \left (\ln \left (x +8\right )-4\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 21, normalized size = 0.84 \begin {gather*} x^{3} e^{5} - x^{2} - \log \left (\log \left (x + 8\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 21, normalized size = 0.84 \begin {gather*} x^3\,{\mathrm {e}}^5-\ln \left (\ln \left (x+8\right )-4\right )-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 17, normalized size = 0.68 \begin {gather*} x^{3} e^{5} - x^{2} - \log {\left (\log {\left (x + 8 \right )} - 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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