Optimal. Leaf size=32 \[ 2 \left (e^2+e^5\right )-x-\log \left (\frac {2 \left (e^{e^{4 x^2}}+x\right )}{x}\right ) \]
________________________________________________________________________________________
Rubi [F] time = 1.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-x^2+e^{e^{4 x^2}} \left (1-x-8 e^{4 x^2} x^2\right )}{e^{e^{4 x^2}} x+x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {8 e^{e^{4 x^2}+4 x^2} x}{e^{e^{4 x^2}}+x}-\frac {-e^{e^{4 x^2}}+e^{e^{4 x^2}} x+x^2}{x \left (e^{e^{4 x^2}}+x\right )}\right ) \, dx\\ &=-\left (8 \int \frac {e^{e^{4 x^2}+4 x^2} x}{e^{e^{4 x^2}}+x} \, dx\right )-\int \frac {-e^{e^{4 x^2}}+e^{e^{4 x^2}} x+x^2}{x \left (e^{e^{4 x^2}}+x\right )} \, dx\\ &=-\left (8 \int \frac {e^{e^{4 x^2}+4 x^2} x}{e^{e^{4 x^2}}+x} \, dx\right )-\int \frac {e^{e^{4 x^2}} (-1+x)+x^2}{x \left (e^{e^{4 x^2}}+x\right )} \, dx\\ &=-\left (8 \int \frac {e^{e^{4 x^2}+4 x^2} x}{e^{e^{4 x^2}}+x} \, dx\right )-\int \left (\frac {-1+x}{x}+\frac {1}{e^{e^{4 x^2}}+x}\right ) \, dx\\ &=-\left (8 \int \frac {e^{e^{4 x^2}+4 x^2} x}{e^{e^{4 x^2}}+x} \, dx\right )-\int \frac {-1+x}{x} \, dx-\int \frac {1}{e^{e^{4 x^2}}+x} \, dx\\ &=-\left (8 \int \frac {e^{e^{4 x^2}+4 x^2} x}{e^{e^{4 x^2}}+x} \, dx\right )-\int \left (1-\frac {1}{x}\right ) \, dx-\int \frac {1}{e^{e^{4 x^2}}+x} \, dx\\ &=-x+\log (x)-8 \int \frac {e^{e^{4 x^2}+4 x^2} x}{e^{e^{4 x^2}}+x} \, dx-\int \frac {1}{e^{e^{4 x^2}}+x} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.15, size = 20, normalized size = 0.62 \begin {gather*} -x+\log (x)-\log \left (e^{e^{4 x^2}}+x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.95, size = 18, normalized size = 0.56 \begin {gather*} -x - \log \left (x + e^{\left (e^{\left (4 \, x^{2}\right )}\right )}\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 36, normalized size = 1.12 \begin {gather*} 4 \, x^{2} - x - \log \left (x e^{\left (4 \, x^{2}\right )} + e^{\left (4 \, x^{2} + e^{\left (4 \, x^{2}\right )}\right )}\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 19, normalized size = 0.59
method | result | size |
norman | \(-x -\ln \left ({\mathrm e}^{{\mathrm e}^{4 x^{2}}}+x \right )+\ln \relax (x )\) | \(19\) |
risch | \(-x -\ln \left ({\mathrm e}^{{\mathrm e}^{4 x^{2}}}+x \right )+\ln \relax (x )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 18, normalized size = 0.56 \begin {gather*} -x - \log \left (x + e^{\left (e^{\left (4 \, x^{2}\right )}\right )}\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.11, size = 18, normalized size = 0.56 \begin {gather*} \ln \relax (x)-\ln \left (x+{\mathrm {e}}^{{\mathrm {e}}^{4\,x^2}}\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.29, size = 15, normalized size = 0.47 \begin {gather*} - x + \log {\relax (x )} - \log {\left (x + e^{e^{4 x^{2}}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________