Optimal. Leaf size=15 \[ 5 \left (-20-3 x+\log ^2(3+e x)\right ) \]
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Rubi [A]
time = 0.08, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps
used = 6, number of rules used = 5, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.217, Rules used = {6873, 12, 6874,
2437, 2338} \begin {gather*} 5 \log ^2(e x+3)-15 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2338
Rule 2437
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 (-9-3 e x+2 e \log (3+e x))}{3+e x} \, dx\\ &=5 \int \frac {-9-3 e x+2 e \log (3+e x)}{3+e x} \, dx\\ &=5 \int \left (-3+\frac {2 e \log (3+e x)}{3+e x}\right ) \, dx\\ &=-15 x+(10 e) \int \frac {\log (3+e x)}{3+e x} \, dx\\ &=-15 x+10 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,3+e x\right )\\ &=-15 x+5 \log ^2(3+e x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 16, normalized size = 1.07 \begin {gather*} -5 \left (3 x-\log ^2(3+e x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 26, normalized size = 1.73
method | result | size |
norman | \(-15 x +5 \ln \left (x \,{\mathrm e}+3\right )^{2}\) | \(16\) |
risch | \(-15 x +5 \ln \left (x \,{\mathrm e}+3\right )^{2}\) | \(16\) |
derivativedivides | \(5 \,{\mathrm e}^{-1} \left ({\mathrm e} \ln \left (x \,{\mathrm e}+3\right )^{2}-3 x \,{\mathrm e}-9\right )\) | \(26\) |
default | \(5 \,{\mathrm e}^{-1} \left ({\mathrm e} \ln \left (x \,{\mathrm e}+3\right )^{2}-3 x \,{\mathrm e}-9\right )\) | \(26\) |
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. 43 vs.
\(2 (16) = 32\).
time = 0.26, size = 43, normalized size = 2.87 \begin {gather*} -15 \, {\left (x e^{\left (-1\right )} - 3 \, e^{\left (-2\right )} \log \left (x e + 3\right )\right )} e - 45 \, e^{\left (-1\right )} \log \left (x e + 3\right ) + 5 \, \log \left (x e + 3\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 15, normalized size = 1.00 \begin {gather*} 5 \, \log \left (x e + 3\right )^{2} - 15 \, 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 = 0.93 \begin {gather*} - 15 x + 5 \log {\left (e x + 3 \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 1.00 \begin {gather*} 5 \, \log \left (x e + 3\right )^{2} - 15 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.25, size = 15, normalized size = 1.00 \begin {gather*} 5\,{\ln \left (x\,\mathrm {e}+3\right )}^2-15\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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