Optimal. Leaf size=16 \[ x \left (-901-e^{5 x}+x-\log (x)\right ) \]
________________________________________________________________________________________
Rubi [B] time = 0.02, antiderivative size = 35, normalized size of antiderivative = 2.19, number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {2176, 2194, 2295} \begin {gather*} x^2-901 x+\frac {e^{5 x}}{5}-\frac {1}{5} e^{5 x} (5 x+1)-x \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2176
Rule 2194
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-902 x+x^2+\int e^{5 x} (-1-5 x) \, dx-\int \log (x) \, dx\\ &=-901 x+x^2-\frac {1}{5} e^{5 x} (1+5 x)-x \log (x)+\int e^{5 x} \, dx\\ &=\frac {e^{5 x}}{5}-901 x+x^2-\frac {1}{5} e^{5 x} (1+5 x)-x \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 20, normalized size = 1.25 \begin {gather*} -901 x-e^{5 x} x+x^2-x \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.71, size = 19, normalized size = 1.19 \begin {gather*} x^{2} - x e^{\left (5 \, x\right )} - x \log \relax (x) - 901 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.23, size = 19, normalized size = 1.19 \begin {gather*} x^{2} - x e^{\left (5 \, x\right )} - x \log \relax (x) - 901 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 20, normalized size = 1.25
method | result | size |
default | \(-901 x -x \,{\mathrm e}^{5 x}+x^{2}-x \ln \relax (x )\) | \(20\) |
norman | \(-901 x -x \,{\mathrm e}^{5 x}+x^{2}-x \ln \relax (x )\) | \(20\) |
risch | \(-901 x -x \,{\mathrm e}^{5 x}+x^{2}-x \ln \relax (x )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.36, size = 19, normalized size = 1.19 \begin {gather*} x^{2} - x e^{\left (5 \, x\right )} - x \log \relax (x) - 901 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.89, size = 14, normalized size = 0.88 \begin {gather*} -x\,\left ({\mathrm {e}}^{5\,x}-x+\ln \relax (x)+901\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.25, size = 17, normalized size = 1.06 \begin {gather*} x^{2} - x e^{5 x} - x \log {\relax (x )} - 901 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________