Optimal. Leaf size=20 \[ 4+e^3-e^5 x+x^2-\frac {1}{\log (x)} \]
________________________________________________________________________________________
Rubi [A] time = 0.09, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 4, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {6688, 2302, 30} \begin {gather*} x^2-e^5 x-\frac {1}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 30
Rule 2302
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^5+2 x+\frac {1}{x \log ^2(x)}\right ) \, dx\\ &=-e^5 x+x^2+\int \frac {1}{x \log ^2(x)} \, dx\\ &=-e^5 x+x^2+\operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right )\\ &=-e^5 x+x^2-\frac {1}{\log (x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 0.80 \begin {gather*} -e^5 x+x^2-\frac {1}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.59, size = 19, normalized size = 0.95 \begin {gather*} \frac {{\left (x^{2} - x e^{5}\right )} \log \relax (x) - 1}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.12, size = 20, normalized size = 1.00 \begin {gather*} \frac {x^{2} \log \relax (x) - x e^{5} \log \relax (x) - 1}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 16, normalized size = 0.80
method | result | size |
default | \(-x \,{\mathrm e}^{5}+x^{2}-\frac {1}{\ln \relax (x )}\) | \(16\) |
risch | \(-x \,{\mathrm e}^{5}+x^{2}-\frac {1}{\ln \relax (x )}\) | \(16\) |
norman | \(\frac {-1+x^{2} \ln \relax (x )-x \,{\mathrm e}^{5} \ln \relax (x )}{\ln \relax (x )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 15, normalized size = 0.75 \begin {gather*} x^{2} - x e^{5} - \frac {1}{\log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 6.79, size = 15, normalized size = 0.75 \begin {gather*} x\,\left (x-{\mathrm {e}}^5\right )-\frac {1}{\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 12, normalized size = 0.60 \begin {gather*} x^{2} - x e^{5} - \frac {1}{\log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________