Optimal. Leaf size=19 \[ \frac {16 e^{2+4 x+4 x^2} x}{\log ^8(x)} \]
________________________________________________________________________________________
Rubi [F] time = 0.60, 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 {16 e^{2+4 x+4 x^2} \left (-8+\left (1+4 x+8 x^2\right ) \log (x)\right )}{\log ^9(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=16 \int \frac {e^{2+4 x+4 x^2} \left (-8+\left (1+4 x+8 x^2\right ) \log (x)\right )}{\log ^9(x)} \, dx\\ &=16 \int \left (-\frac {8 e^{2+4 x+4 x^2}}{\log ^9(x)}+\frac {e^{2+4 x+4 x^2} \left (1+4 x+8 x^2\right )}{\log ^8(x)}\right ) \, dx\\ &=16 \int \frac {e^{2+4 x+4 x^2} \left (1+4 x+8 x^2\right )}{\log ^8(x)} \, dx-128 \int \frac {e^{2+4 x+4 x^2}}{\log ^9(x)} \, dx\\ &=16 \int \left (\frac {e^{2+4 x+4 x^2}}{\log ^8(x)}+\frac {4 e^{2+4 x+4 x^2} x}{\log ^8(x)}+\frac {8 e^{2+4 x+4 x^2} x^2}{\log ^8(x)}\right ) \, dx-128 \int \frac {e^{2+4 x+4 x^2}}{\log ^9(x)} \, dx\\ &=16 \int \frac {e^{2+4 x+4 x^2}}{\log ^8(x)} \, dx+64 \int \frac {e^{2+4 x+4 x^2} x}{\log ^8(x)} \, dx-128 \int \frac {e^{2+4 x+4 x^2}}{\log ^9(x)} \, dx+128 \int \frac {e^{2+4 x+4 x^2} x^2}{\log ^8(x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.13, size = 19, normalized size = 1.00 \begin {gather*} \frac {16 e^{2+4 x+4 x^2} x}{\log ^8(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 18, normalized size = 0.95 \begin {gather*} \frac {16 \, x e^{\left (4 \, x^{2} + 4 \, x + 2\right )}}{\log \relax (x)^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 18, normalized size = 0.95 \begin {gather*} \frac {16 \, x e^{\left (4 \, x^{2} + 4 \, x + 2\right )}}{\log \relax (x)^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.10, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (8 x^{2}+4 x +1\right ) \ln \relax (x )-8\right ) {\mathrm e}^{-\ln \left (\frac {\ln \relax (x )^{8} {\mathrm e}^{-4 x} {\mathrm e}^{-4 x^{2}}}{16}\right )+2}}{\ln \relax (x )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 18, normalized size = 0.95 \begin {gather*} \frac {16 \, x e^{\left (4 \, x^{2} + 4 \, x + 2\right )}}{\log \relax (x)^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.52, size = 19, normalized size = 1.00 \begin {gather*} \frac {16\,x\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{4\,x^2}}{{\ln \relax (x)}^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.34, size = 22, normalized size = 1.16 \begin {gather*} \frac {16 x e^{2} e^{4 x} e^{4 x^{2}}}{\log {\relax (x )}^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________