Optimal. Leaf size=22 \[ \frac {e^x \left (25+\frac {3}{5 x-\log (x)}\right )}{\log (9)} \]
________________________________________________________________________________________
Rubi [B] time = 0.35, antiderivative size = 49, normalized size of antiderivative = 2.23, number of steps used = 3, number of rules used = 3, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {6688, 12, 2288} \begin {gather*} \frac {e^x \left (625 x^3+15 x^2+25 x \log ^2(x)-(250 x+3) x \log (x)\right )}{x \log (9) (5 x-\log (x))^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2288
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x \left (3-15 x+15 x^2+625 x^3-x (3+250 x) \log (x)+25 x \log ^2(x)\right )}{x \log (9) (5 x-\log (x))^2} \, dx\\ &=\frac {\int \frac {e^x \left (3-15 x+15 x^2+625 x^3-x (3+250 x) \log (x)+25 x \log ^2(x)\right )}{x (5 x-\log (x))^2} \, dx}{\log (9)}\\ &=\frac {e^x \left (15 x^2+625 x^3-x (3+250 x) \log (x)+25 x \log ^2(x)\right )}{x \log (9) (5 x-\log (x))^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.09, size = 27, normalized size = 1.23 \begin {gather*} \frac {e^x (3+125 x-25 \log (x))}{\log (9) (5 x-\log (x))} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.73, size = 31, normalized size = 1.41 \begin {gather*} \frac {{\left (125 \, x + 3\right )} e^{x} - 25 \, e^{x} \log \relax (x)}{2 \, {\left (5 \, x \log \relax (3) - \log \relax (3) \log \relax (x)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 32, normalized size = 1.45 \begin {gather*} \frac {125 \, x e^{x} - 25 \, e^{x} \log \relax (x) + 3 \, e^{x}}{2 \, {\left (5 \, x \log \relax (3) - \log \relax (3) \log \relax (x)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 28, normalized size = 1.27
method | result | size |
risch | \(\frac {25 \,{\mathrm e}^{x}}{2 \ln \relax (3)}+\frac {3 \,{\mathrm e}^{x}}{2 \ln \relax (3) \left (-\ln \relax (x )+5 x \right )}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 27, normalized size = 1.23 \begin {gather*} \frac {{\left (125 \, x - 25 \, \log \relax (x) + 3\right )} e^{x}}{2 \, {\left (5 \, x \log \relax (3) - \log \relax (3) \log \relax (x)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.71, size = 27, normalized size = 1.23 \begin {gather*} \frac {{\mathrm {e}}^x\,\left (125\,x-25\,\ln \relax (x)+3\right )}{2\,\ln \relax (3)\,\left (5\,x-\ln \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.31, size = 27, normalized size = 1.23 \begin {gather*} \frac {\left (125 x - 25 \log {\relax (x )} + 3\right ) e^{x}}{10 x \log {\relax (3 )} - 2 \log {\relax (3 )} \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________