Optimal. Leaf size=13 \[ x \left (-5+e^x (1+x)\right ) \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.07, antiderivative size = 22, normalized size of antiderivative = 1.69, number of steps
used = 7, number of rules used = 4, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2207, 2225,
2227, 2634} \begin {gather*} e^x x^2 \log (x)+e^x x \log (x)-5 x \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2207
Rule 2225
Rule 2227
Rule 2634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-5 x+\int e^x (1+x) \, dx+\int \left (-5+e^x \left (1+3 x+x^2\right )\right ) \log (x) \, dx\\ &=-5 x+e^x (1+x)-5 x \log (x)+e^x x \log (x)+e^x x^2 \log (x)-\int e^x \, dx-\int \left (-5+e^x (1+x)\right ) \, dx\\ &=-e^x+e^x (1+x)-5 x \log (x)+e^x x \log (x)+e^x x^2 \log (x)-\int e^x (1+x) \, dx\\ &=-e^x-5 x \log (x)+e^x x \log (x)+e^x x^2 \log (x)+\int e^x \, dx\\ &=-5 x \log (x)+e^x x \log (x)+e^x x^2 \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 14, normalized size = 1.08 \begin {gather*} x \left (-5+e^x+e^x x\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.04, size = 21, normalized size = 1.62
method | result | size |
risch | \(x \left ({\mathrm e}^{x} x +{\mathrm e}^{x}-5\right ) \ln \left (x \right )\) | \(13\) |
default | \(x^{2} {\mathrm e}^{x} \ln \left (x \right )+x \,{\mathrm e}^{x} \ln \left (x \right )-5 x \ln \left (x \right )\) | \(21\) |
norman | \(x^{2} {\mathrm e}^{x} \ln \left (x \right )+x \,{\mathrm e}^{x} \ln \left (x \right )-5 x \ln \left (x \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 29 vs.
\(2 (12) = 24\).
time = 0.29, size = 29, normalized size = 2.23 \begin {gather*} {\left (x - 1\right )} e^{x} - x e^{x} + {\left ({\left (x^{2} + x\right )} e^{x} - 5 \, x\right )} \log \left (x\right ) + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 15, normalized size = 1.15 \begin {gather*} {\left ({\left (x^{2} + x\right )} e^{x} - 5 \, x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 20, normalized size = 1.54 \begin {gather*} - 5 x \log {\left (x \right )} + \left (x^{2} \log {\left (x \right )} + x \log {\left (x \right )}\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 31 vs.
\(2 (12) = 24\).
time = 0.42, size = 31, normalized size = 2.38 \begin {gather*} -{\left (x - 1\right )} e^{x} + x e^{x} + {\left ({\left (x^{2} + x\right )} e^{x} - 5 \, x\right )} \log \left (x\right ) - e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.31, size = 12, normalized size = 0.92 \begin {gather*} x\,\ln \left (x\right )\,\left ({\mathrm {e}}^x+x\,{\mathrm {e}}^x-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________