Optimal. Leaf size=10 \[ e^{3+x^3} \log (x) \]
________________________________________________________________________________________
Rubi [A] time = 0.09, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.192, Rules used = {14, 2210, 2209, 2554, 12} \begin {gather*} e^{x^3+3} \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 2209
Rule 2210
Rule 2554
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^{3+x^3}}{x}+3 e^{3+x^3} x^2 \log (x)\right ) \, dx\\ &=3 \int e^{3+x^3} x^2 \log (x) \, dx+\int \frac {e^{3+x^3}}{x} \, dx\\ &=\frac {e^3 \text {Ei}\left (x^3\right )}{3}+e^{3+x^3} \log (x)-3 \int \frac {e^{3+x^3}}{3 x} \, dx\\ &=\frac {e^3 \text {Ei}\left (x^3\right )}{3}+e^{3+x^3} \log (x)-\int \frac {e^{3+x^3}}{x} \, dx\\ &=e^{3+x^3} \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 10, normalized size = 1.00 \begin {gather*} e^{3+x^3} \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 9, normalized size = 0.90 \begin {gather*} e^{\left (x^{3} + 3\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.20, size = 9, normalized size = 0.90 \begin {gather*} e^{\left (x^{3} + 3\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 10, normalized size = 1.00
method | result | size |
norman | \({\mathrm e}^{x^{3}+3} \ln \relax (x )\) | \(10\) |
risch | \({\mathrm e}^{x^{3}+3} \ln \relax (x )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.40, size = 9, normalized size = 0.90 \begin {gather*} e^{\left (x^{3} + 3\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.59, size = 9, normalized size = 0.90 \begin {gather*} {\mathrm {e}}^{x^3}\,{\mathrm {e}}^3\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.27, size = 8, normalized size = 0.80 \begin {gather*} e^{x^{3} + 3} \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________