Optimal. Leaf size=21 \[ \log \left (-5+9 e^{\frac {x^4}{\left (4+e^3 x\right )^2}}+x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.47, antiderivative size = 23, normalized size of antiderivative = 1.10, number of steps
used = 2, number of rules used = 2, integrand size = 149, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6820, 6816}
\begin {gather*} \log \left (-9 e^{\frac {x^4}{\left (e^3 x+4\right )^2}}-x+5\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6816
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-64-48 e^3 x-12 e^6 x^2-e^9 x^3-144 e^{\frac {x^4}{\left (4+e^3 x\right )^2}} x^3-18 e^{3+\frac {x^4}{\left (4+e^3 x\right )^2}} x^4}{\left (5-9 e^{\frac {x^4}{\left (4+e^3 x\right )^2}}-x\right ) \left (4+e^3 x\right )^3} \, dx\\ &=\log \left (5-9 e^{\frac {x^4}{\left (4+e^3 x\right )^2}}-x\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(57\) vs. \(2(21)=42\).
time = 0.13, size = 57, normalized size = 2.71 \begin {gather*} \log \left (5-9 e^{\frac {48}{e^{12}}-\frac {8 x}{e^9}+\frac {x^2}{e^6}+\frac {256}{e^{12} \left (4+e^3 x\right )^2}-\frac {256}{e^{12} \left (4+e^3 x\right )}}-x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.13, size = 29, normalized size = 1.38
method | result | size |
norman | \(\ln \left (x +9 \,{\mathrm e}^{\frac {x^{4}}{x^{2} {\mathrm e}^{6}+8 x \,{\mathrm e}^{3}+16}}-5\right )\) | \(29\) |
risch | \({\mathrm e}^{3} {\mathrm e}^{-9} x^{2}-8 x \,{\mathrm e}^{-9}+\frac {\left (-256 x -768 \,{\mathrm e}^{-3}\right ) {\mathrm e}^{-9}}{x^{2} {\mathrm e}^{6}+8 x \,{\mathrm e}^{3}+16}-\frac {x^{4}}{x^{2} {\mathrm e}^{6}+8 x \,{\mathrm e}^{3}+16}+\ln \left ({\mathrm e}^{\frac {x^{4}}{x^{2} {\mathrm e}^{6}+8 x \,{\mathrm e}^{3}+16}}+\frac {x}{9}-\frac {5}{9}\right )\) | \(87\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 108 vs.
\(2 (20) = 40\).
time = 0.32, size = 108, normalized size = 5.14 \begin {gather*} \frac {x^{3} e^{9} - 4 \, x^{2} e^{6} - 32 \, x e^{3} - 256}{x e^{15} + 4 \, e^{12}} + \log \left (\frac {1}{9} \, {\left ({\left (x - 5\right )} e^{\left (8 \, x e^{\left (-9\right )} + \frac {256}{x e^{15} + 4 \, e^{12}}\right )} + 9 \, e^{\left (x^{2} e^{\left (-6\right )} + \frac {256}{x^{2} e^{18} + 8 \, x e^{15} + 16 \, e^{12}} + 48 \, e^{\left (-12\right )}\right )}\right )} e^{\left (-x^{2} e^{\left (-6\right )} - 48 \, e^{\left (-12\right )}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 26, normalized size = 1.24 \begin {gather*} \log \left (x + 9 \, e^{\left (\frac {x^{4}}{x^{2} e^{6} + 8 \, x e^{3} + 16}\right )} - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.36, size = 27, normalized size = 1.29 \begin {gather*} \log {\left (\frac {x}{9} + e^{\frac {x^{4}}{x^{2} e^{6} + 8 x e^{3} + 16}} - \frac {5}{9} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.48, size = 26, normalized size = 1.24 \begin {gather*} \log \left (x + 9 \, e^{\left (\frac {x^{4}}{x^{2} e^{6} + 8 \, x e^{3} + 16}\right )} - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 8.57, size = 19, normalized size = 0.90 \begin {gather*} \ln \left (x+9\,{\mathrm {e}}^{\frac {x^4}{{\left (x\,{\mathrm {e}}^3+4\right )}^2}}-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________