Optimal. Leaf size=18 \[ e^{2 e^5}+\frac {3+\log (4+x)}{x^2} \]
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Rubi [A]
time = 0.16, antiderivative size = 14, normalized size of antiderivative = 0.78, number of steps
used = 8, number of rules used = 5, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.185, Rules used = {1607, 6874, 78,
2442, 46} \begin {gather*} \frac {3}{x^2}+\frac {\log (x+4)}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 46
Rule 78
Rule 1607
Rule 2442
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-24-5 x+(-8-2 x) \log (4+x)}{x^3 (4+x)} \, dx\\ &=\int \left (\frac {-24-5 x}{x^3 (4+x)}-\frac {2 \log (4+x)}{x^3}\right ) \, dx\\ &=-\left (2 \int \frac {\log (4+x)}{x^3} \, dx\right )+\int \frac {-24-5 x}{x^3 (4+x)} \, dx\\ &=\frac {\log (4+x)}{x^2}-\int \frac {1}{x^2 (4+x)} \, dx+\int \left (-\frac {6}{x^3}+\frac {1}{4 x^2}-\frac {1}{16 x}+\frac {1}{16 (4+x)}\right ) \, dx\\ &=\frac {3}{x^2}-\frac {1}{4 x}-\frac {\log (x)}{16}+\frac {1}{16} \log (4+x)+\frac {\log (4+x)}{x^2}-\int \left (\frac {1}{4 x^2}-\frac {1}{16 x}+\frac {1}{16 (4+x)}\right ) \, dx\\ &=\frac {3}{x^2}+\frac {\log (4+x)}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 14, normalized size = 0.78 \begin {gather*} \frac {3}{x^2}+\frac {\log (4+x)}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 28, normalized size = 1.56
method | result | size |
norman | \(\frac {3+\ln \left (4+x \right )}{x^{2}}\) | \(11\) |
risch | \(\frac {\ln \left (4+x \right )}{x^{2}}+\frac {3}{x^{2}}\) | \(15\) |
derivativedivides | \(-\frac {\ln \left (4+x \right ) \left (4+x \right ) \left (x -4\right )}{16 x^{2}}+\frac {3}{x^{2}}+\frac {\ln \left (4+x \right )}{16}\) | \(28\) |
default | \(-\frac {\ln \left (4+x \right ) \left (4+x \right ) \left (x -4\right )}{16 x^{2}}+\frac {3}{x^{2}}+\frac {\ln \left (4+x \right )}{16}\) | \(28\) |
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. 39 vs.
\(2 (16) = 32\).
time = 0.29, size = 39, normalized size = 2.17 \begin {gather*} -\frac {{\left (x^{2} - 16\right )} \log \left (x + 4\right ) - 4 \, x}{16 \, x^{2}} - \frac {3 \, {\left (x - 2\right )}}{2 \, x^{2}} + \frac {5}{4 \, x} + \frac {1}{16} \, \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 10, normalized size = 0.56 \begin {gather*} \frac {\log \left (x + 4\right ) + 3}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.67 \begin {gather*} \frac {\log {\left (x + 4 \right )}}{x^{2}} + \frac {3}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 14, normalized size = 0.78 \begin {gather*} \frac {\log \left (x + 4\right )}{x^{2}} + \frac {3}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.94, size = 10, normalized size = 0.56 \begin {gather*} \frac {\ln \left (x+4\right )+3}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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