Optimal. Leaf size=23 \[ 5 e^{x^2} \left (20+x-x \left (-2-\log ^2(x)\right )\right )^2 \]
________________________________________________________________________________________
Rubi [F] time = 0.79, 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 \left (e^{x^2} \left (600+4090 x+1200 x^2+90 x^3\right )+e^{x^2} (400+60 x) \log (x)+e^{x^2} \left (200+60 x+400 x^2+60 x^3\right ) \log ^2(x)+20 e^{x^2} x \log ^3(x)+e^{x^2} \left (10 x+10 x^3\right ) \log ^4(x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=20 \int e^{x^2} x \log ^3(x) \, dx+\int e^{x^2} \left (600+4090 x+1200 x^2+90 x^3\right ) \, dx+\int e^{x^2} (400+60 x) \log (x) \, dx+\int e^{x^2} \left (200+60 x+400 x^2+60 x^3\right ) \log ^2(x) \, dx+\int e^{x^2} \left (10 x+10 x^3\right ) \log ^4(x) \, dx\\ &=30 e^{x^2} \log (x)+200 \sqrt {\pi } \text {erfi}(x) \log (x)+20 \int e^{x^2} x \log ^3(x) \, dx+\int \left (600 e^{x^2}+4090 e^{x^2} x+1200 e^{x^2} x^2+90 e^{x^2} x^3\right ) \, dx-\int \frac {10 \left (3 e^{x^2}+20 \sqrt {\pi } \text {erfi}(x)\right )}{x} \, dx+\int e^{x^2} x \left (10+10 x^2\right ) \log ^4(x) \, dx+\int \left (200 e^{x^2} \log ^2(x)+60 e^{x^2} x \log ^2(x)+400 e^{x^2} x^2 \log ^2(x)+60 e^{x^2} x^3 \log ^2(x)\right ) \, dx\\ &=30 e^{x^2} \log (x)+200 \sqrt {\pi } \text {erfi}(x) \log (x)-10 \int \frac {3 e^{x^2}+20 \sqrt {\pi } \text {erfi}(x)}{x} \, dx+20 \int e^{x^2} x \log ^3(x) \, dx+60 \int e^{x^2} x \log ^2(x) \, dx+60 \int e^{x^2} x^3 \log ^2(x) \, dx+90 \int e^{x^2} x^3 \, dx+200 \int e^{x^2} \log ^2(x) \, dx+400 \int e^{x^2} x^2 \log ^2(x) \, dx+600 \int e^{x^2} \, dx+1200 \int e^{x^2} x^2 \, dx+4090 \int e^{x^2} x \, dx+\int \left (10 e^{x^2} x \log ^4(x)+10 e^{x^2} x^3 \log ^4(x)\right ) \, dx\\ &=2045 e^{x^2}+600 e^{x^2} x+45 e^{x^2} x^2+300 \sqrt {\pi } \text {erfi}(x)+30 e^{x^2} \log (x)+200 \sqrt {\pi } \text {erfi}(x) \log (x)-10 \int \left (\frac {3 e^{x^2}}{x}+\frac {20 \sqrt {\pi } \text {erfi}(x)}{x}\right ) \, dx+10 \int e^{x^2} x \log ^4(x) \, dx+10 \int e^{x^2} x^3 \log ^4(x) \, dx+20 \int e^{x^2} x \log ^3(x) \, dx+60 \int e^{x^2} x \log ^2(x) \, dx+60 \int e^{x^2} x^3 \log ^2(x) \, dx-90 \int e^{x^2} x \, dx+200 \int e^{x^2} \log ^2(x) \, dx+400 \int e^{x^2} x^2 \log ^2(x) \, dx-600 \int e^{x^2} \, dx\\ &=2000 e^{x^2}+600 e^{x^2} x+45 e^{x^2} x^2+30 e^{x^2} \log (x)+200 \sqrt {\pi } \text {erfi}(x) \log (x)+10 \int e^{x^2} x \log ^4(x) \, dx+10 \int e^{x^2} x^3 \log ^4(x) \, dx+20 \int e^{x^2} x \log ^3(x) \, dx-30 \int \frac {e^{x^2}}{x} \, dx+60 \int e^{x^2} x \log ^2(x) \, dx+60 \int e^{x^2} x^3 \log ^2(x) \, dx+200 \int e^{x^2} \log ^2(x) \, dx+400 \int e^{x^2} x^2 \log ^2(x) \, dx-\left (200 \sqrt {\pi }\right ) \int \frac {\text {erfi}(x)}{x} \, dx\\ &=2000 e^{x^2}+600 e^{x^2} x+45 e^{x^2} x^2-15 \text {Ei}\left (x^2\right )-400 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )+30 e^{x^2} \log (x)+200 \sqrt {\pi } \text {erfi}(x) \log (x)+10 \int e^{x^2} x \log ^4(x) \, dx+10 \int e^{x^2} x^3 \log ^4(x) \, dx+20 \int e^{x^2} x \log ^3(x) \, dx+60 \int e^{x^2} x \log ^2(x) \, dx+60 \int e^{x^2} x^3 \log ^2(x) \, dx+200 \int e^{x^2} \log ^2(x) \, dx+400 \int e^{x^2} x^2 \log ^2(x) \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.76, size = 20, normalized size = 0.87 \begin {gather*} 5 e^{x^2} \left (20+3 x+x \log ^2(x)\right )^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.70, size = 49, normalized size = 2.13 \begin {gather*} 5 \, x^{2} e^{\left (x^{2}\right )} \log \relax (x)^{4} + 10 \, {\left (3 \, x^{2} + 20 \, x\right )} e^{\left (x^{2}\right )} \log \relax (x)^{2} + 5 \, {\left (9 \, x^{2} + 120 \, x + 400\right )} e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.38, size = 57, normalized size = 2.48 \begin {gather*} 5 \, {\left ({\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} + e^{\left (x^{2}\right )}\right )} \log \relax (x)^{4} + 10 \, {\left (3 \, x^{2} + 20 \, x\right )} e^{\left (x^{2}\right )} \log \relax (x)^{2} + 5 \, {\left (9 \, x^{2} + 120 \, x + 400\right )} e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.13, size = 46, normalized size = 2.00
method | result | size |
risch | \(\left (45 x^{2}+600 x +2000\right ) {\mathrm e}^{x^{2}}+5 x^{2} {\mathrm e}^{x^{2}} \ln \relax (x )^{4}+10 x \left (3 x +20\right ) {\mathrm e}^{x^{2}} \ln \relax (x )^{2}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.50, size = 55, normalized size = 2.39 \begin {gather*} 5 \, {\left (x^{2} \log \relax (x)^{4} + 2 \, {\left (3 \, x^{2} + 20 \, x\right )} \log \relax (x)^{2}\right )} e^{\left (x^{2}\right )} + 45 \, {\left (x^{2} - 1\right )} e^{\left (x^{2}\right )} + 600 \, x e^{\left (x^{2}\right )} + 2045 \, e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int {\mathrm {e}}^{x^2}\,\left (10\,x^3+10\,x\right )\,{\ln \relax (x)}^4+20\,x\,{\mathrm {e}}^{x^2}\,{\ln \relax (x)}^3+{\mathrm {e}}^{x^2}\,\left (60\,x^3+400\,x^2+60\,x+200\right )\,{\ln \relax (x)}^2+{\mathrm {e}}^{x^2}\,\left (60\,x+400\right )\,\ln \relax (x)+{\mathrm {e}}^{x^2}\,\left (90\,x^3+1200\,x^2+4090\,x+600\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.45, size = 42, normalized size = 1.83 \begin {gather*} \left (5 x^{2} \log {\relax (x )}^{4} + 30 x^{2} \log {\relax (x )}^{2} + 45 x^{2} + 200 x \log {\relax (x )}^{2} + 600 x + 2000\right ) e^{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________