Optimal. Leaf size=18 \[ 2+2 x-x^4-\frac {1}{\log (4+x)} \]
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Rubi [A] time = 0.17, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 7, number of rules used = 5, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.139, Rules used = {6688, 6742, 2390, 2302, 30} \begin {gather*} -x^4+2 x-\frac {1}{\log (x+4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rule 2302
Rule 2390
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (4+x-8 x^3-2 x^4\right )+\frac {1}{\log ^2(4+x)}}{4+x} \, dx\\ &=\int \left (-2 \left (-1+2 x^3\right )+\frac {1}{(4+x) \log ^2(4+x)}\right ) \, dx\\ &=-\left (2 \int \left (-1+2 x^3\right ) \, dx\right )+\int \frac {1}{(4+x) \log ^2(4+x)} \, dx\\ &=2 x-x^4+\operatorname {Subst}\left (\int \frac {1}{x \log ^2(x)} \, dx,x,4+x\right )\\ &=2 x-x^4+\operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (4+x)\right )\\ &=2 x-x^4-\frac {1}{\log (4+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 17, normalized size = 0.94 \begin {gather*} 2 x-x^4-\frac {1}{\log (4+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 22, normalized size = 1.22 \begin {gather*} -\frac {{\left (x^{4} - 2 \, x\right )} \log \left (x + 4\right ) + 1}{\log \left (x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 17, normalized size = 0.94 \begin {gather*} -x^{4} + 2 \, x - \frac {1}{\log \left (x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 18, normalized size = 1.00
method | result | size |
risch | \(-x^{4}+2 x -\frac {1}{\ln \left (4+x \right )}\) | \(18\) |
norman | \(\frac {-1+2 x \ln \left (4+x \right )-x^{4} \ln \left (4+x \right )}{\ln \left (4+x \right )}\) | \(26\) |
derivativedivides | \(-\left (4+x \right )^{4}+16 \left (4+x \right )^{3}-96 \left (4+x \right )^{2}+1032+258 x -\frac {1}{\ln \left (4+x \right )}\) | \(35\) |
default | \(-\left (4+x \right )^{4}+16 \left (4+x \right )^{3}-96 \left (4+x \right )^{2}+1032+258 x -\frac {1}{\ln \left (4+x \right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 17, normalized size = 0.94 \begin {gather*} -x^{4} + 2 \, x - \frac {1}{\log \left (x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.26, size = 17, normalized size = 0.94 \begin {gather*} 2\,x-\frac {1}{\ln \left (x+4\right )}-x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 0.67 \begin {gather*} - x^{4} + 2 x - \frac {1}{\log {\left (x + 4 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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