Optimal. Leaf size=18 \[ e^x \left (4+3 x-x^2-\log (x)\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.07, antiderivative size = 27, normalized size of antiderivative = 1.50, number of steps
used = 11, number of rules used = 5, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {14, 2225,
2209, 2207, 2634} \begin {gather*} -e^x x^2+3 e^x x+4 e^x-e^x \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2207
Rule 2209
Rule 2225
Rule 2634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (7 e^x-\frac {e^x}{x}+e^x x-e^x x^2-e^x \log (x)\right ) \, dx\\ &=7 \int e^x \, dx-\int \frac {e^x}{x} \, dx+\int e^x x \, dx-\int e^x x^2 \, dx-\int e^x \log (x) \, dx\\ &=7 e^x+e^x x-e^x x^2-\text {Ei}(x)-e^x \log (x)+2 \int e^x x \, dx-\int e^x \, dx+\int \frac {e^x}{x} \, dx\\ &=6 e^x+3 e^x x-e^x x^2-e^x \log (x)-2 \int e^x \, dx\\ &=4 e^x+3 e^x x-e^x x^2-e^x \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 15, normalized size = 0.83 \begin {gather*} -e^x \left (-4-3 x+x^2+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.28, size = 20, normalized size = 1.11
method | result | size |
risch | \(-{\mathrm e}^{x} \ln \left (x \right )-\left (x^{2}-3 x -4\right ) {\mathrm e}^{x}\) | \(20\) |
norman | \(3 \,{\mathrm e}^{x} x -{\mathrm e}^{x} x^{2}-{\mathrm e}^{x} \ln \left (x \right )+4 \,{\mathrm e}^{x}\) | \(24\) |
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.
\(2 (14) = 28\).
time = 0.32, size = 29, normalized size = 1.61 \begin {gather*} -{\left (x^{2} - 2 \, x + 2\right )} e^{x} + {\left (x - 1\right )} e^{x} - e^{x} \log \left (x\right ) + 7 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.40, size = 19, normalized size = 1.06 \begin {gather*} -{\left (x^{2} - 3 \, x - 4\right )} e^{x} - e^{x} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 14, normalized size = 0.78 \begin {gather*} \left (- x^{2} + 3 x - \log {\left (x \right )} + 4\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.43, size = 23, normalized size = 1.28 \begin {gather*} -x^{2} e^{x} + 3 \, x e^{x} - e^{x} \log \left (x\right ) + 4 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.50, size = 17, normalized size = 0.94 \begin {gather*} {\mathrm {e}}^x\,\left (3\,x-\ln \left (x\right )-x^2+4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________