Optimal. Leaf size=27 \[ -3+\frac {e^{x+(e+x) \left (e^{x^2}+x^2\right )}}{x \log (3)} \]
________________________________________________________________________________________
Rubi [F] time = 3.37, 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 {e^{e x^2+x^3+e^{x^2} (e+x)} \left (e^{x+x^2} \left (x+2 e x^2+2 x^3\right )+e^x \left (-1+x+2 e x^2+3 x^3\right )\right )}{x^2 \log (3)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{e x^2+x^3+e^{x^2} (e+x)} \left (e^{x+x^2} \left (x+2 e x^2+2 x^3\right )+e^x \left (-1+x+2 e x^2+3 x^3\right )\right )}{x^2} \, dx}{\log (3)}\\ &=\frac {\int \frac {e^{(e+x) \left (e^{x^2}+x^2\right )} \left (e^{x+x^2} \left (x+2 e x^2+2 x^3\right )+e^x \left (-1+x+2 e x^2+3 x^3\right )\right )}{x^2} \, dx}{\log (3)}\\ &=\frac {\int \left (\frac {e^{x+x^2+(e+x) \left (e^{x^2}+x^2\right )} \left (1+2 e x+2 x^2\right )}{x}+\frac {e^{x+(e+x) \left (e^{x^2}+x^2\right )} \left (-1+x+2 e x^2+3 x^3\right )}{x^2}\right ) \, dx}{\log (3)}\\ &=\frac {\int \frac {e^{x+x^2+(e+x) \left (e^{x^2}+x^2\right )} \left (1+2 e x+2 x^2\right )}{x} \, dx}{\log (3)}+\frac {\int \frac {e^{x+(e+x) \left (e^{x^2}+x^2\right )} \left (-1+x+2 e x^2+3 x^3\right )}{x^2} \, dx}{\log (3)}\\ &=\frac {\int \left (2 e^{1+x+(e+x) \left (e^{x^2}+x^2\right )}-\frac {e^{x+(e+x) \left (e^{x^2}+x^2\right )}}{x^2}+\frac {e^{x+(e+x) \left (e^{x^2}+x^2\right )}}{x}+3 e^{x+(e+x) \left (e^{x^2}+x^2\right )} x\right ) \, dx}{\log (3)}+\frac {\int \left (2 e^{1+x+x^2+(e+x) \left (e^{x^2}+x^2\right )}+\frac {e^{x+x^2+(e+x) \left (e^{x^2}+x^2\right )}}{x}+2 e^{x+x^2+(e+x) \left (e^{x^2}+x^2\right )} x\right ) \, dx}{\log (3)}\\ &=-\frac {\int \frac {e^{x+(e+x) \left (e^{x^2}+x^2\right )}}{x^2} \, dx}{\log (3)}+\frac {\int \frac {e^{x+(e+x) \left (e^{x^2}+x^2\right )}}{x} \, dx}{\log (3)}+\frac {\int \frac {e^{x+x^2+(e+x) \left (e^{x^2}+x^2\right )}}{x} \, dx}{\log (3)}+\frac {2 \int e^{1+x+(e+x) \left (e^{x^2}+x^2\right )} \, dx}{\log (3)}+\frac {2 \int e^{1+x+x^2+(e+x) \left (e^{x^2}+x^2\right )} \, dx}{\log (3)}+\frac {2 \int e^{x+x^2+(e+x) \left (e^{x^2}+x^2\right )} x \, dx}{\log (3)}+\frac {3 \int e^{x+(e+x) \left (e^{x^2}+x^2\right )} x \, dx}{\log (3)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.42, size = 29, normalized size = 1.07 \begin {gather*} \frac {e^{x+e x^2+x^3+e^{x^2} (e+x)}}{x \log (3)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.64, size = 29, normalized size = 1.07 \begin {gather*} \frac {e^{\left (x^{3} + x^{2} e + {\left (x + e\right )} e^{\left (x^{2}\right )} + x\right )}}{x \log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left ({\left (2 \, x^{3} + 2 \, x^{2} e + x\right )} e^{\left (x^{2} + x\right )} + {\left (3 \, x^{3} + 2 \, x^{2} e + x - 1\right )} e^{x}\right )} e^{\left (x^{3} + x^{2} e + {\left (x + e\right )} e^{\left (x^{2}\right )}\right )}}{x^{2} \log \relax (3)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.09, size = 34, normalized size = 1.26
method | result | size |
risch | \(\frac {{\mathrm e}^{x^{2} {\mathrm e}+x^{3}+{\mathrm e} \,{\mathrm e}^{x^{2}}+{\mathrm e}^{x^{2}} x +x}}{x \ln \relax (3)}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.51, size = 32, normalized size = 1.19 \begin {gather*} \frac {e^{\left (x^{3} + x^{2} e + x e^{\left (x^{2}\right )} + x + e^{\left (x^{2} + 1\right )}\right )}}{x \log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.56, size = 36, normalized size = 1.33 \begin {gather*} \frac {{\mathrm {e}}^{x^2\,\mathrm {e}}\,{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}\,\mathrm {e}}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{x^2}}\,{\mathrm {e}}^x}{x\,\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.26, size = 29, normalized size = 1.07 \begin {gather*} \frac {e^{x} e^{x^{3} + e x^{2} + \left (x + e\right ) e^{x^{2}}}}{x \log {\relax (3 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________