Optimal. Leaf size=24 \[ -1+e^x+x^2 \left (3+x-9 e^4 x^2 \log ^2(x)\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.088, Rules used = {2194, 2304, 2305} \begin {gather*} -9 e^4 x^4 \log ^2(x)+x^3+3 x^2+e^x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2194
Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3 x^2+x^3-\left (18 e^4\right ) \int x^3 \log (x) \, dx-\left (36 e^4\right ) \int x^3 \log ^2(x) \, dx+\int e^x \, dx\\ &=e^x+3 x^2+x^3+\frac {9 e^4 x^4}{8}-\frac {9}{2} e^4 x^4 \log (x)-9 e^4 x^4 \log ^2(x)+\left (18 e^4\right ) \int x^3 \log (x) \, dx\\ &=e^x+3 x^2+x^3-9 e^4 x^4 \log ^2(x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 24, normalized size = 1.00 \begin {gather*} e^x+3 x^2+x^3-9 e^4 x^4 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.03, size = 22, normalized size = 0.92 \begin {gather*} -9 \, x^{4} e^{4} \log \relax (x)^{2} + x^{3} + 3 \, x^{2} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.36, size = 52, normalized size = 2.17 \begin {gather*} x^{3} + 3 \, x^{2} - \frac {9}{8} \, {\left (8 \, x^{4} \log \relax (x)^{2} - 4 \, x^{4} \log \relax (x) + x^{4}\right )} e^{4} - \frac {9}{8} \, {\left (4 \, x^{4} \log \relax (x) - x^{4}\right )} e^{4} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 23, normalized size = 0.96
method | result | size |
risch | \(x^{3}+3 x^{2}-9 \,{\mathrm e}^{4} x^{4} \ln \relax (x )^{2}+{\mathrm e}^{x}\) | \(23\) |
default | \(x^{3}+3 x^{2}-9 \,{\mathrm e}^{4} x^{4} \ln \relax (x )^{2}+{\mathrm e}^{x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.57, size = 47, normalized size = 1.96 \begin {gather*} -\frac {9}{8} \, {\left (8 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )} x^{4} e^{4} + x^{3} + 3 \, x^{2} - \frac {9}{8} \, {\left (4 \, x^{4} \log \relax (x) - x^{4}\right )} e^{4} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.38, size = 22, normalized size = 0.92 \begin {gather*} {\mathrm {e}}^x+3\,x^2+x^3-9\,x^4\,{\mathrm {e}}^4\,{\ln \relax (x)}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.28, size = 24, normalized size = 1.00 \begin {gather*} - 9 x^{4} e^{4} \log {\relax (x )}^{2} + x^{3} + 3 x^{2} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________