Optimal. Leaf size=34 \[ -3+e^4-x+e^x \left (-2+(2-x)^2-x^2+(4-\log (2))^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 26, normalized size of antiderivative = 0.76, number of steps
used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {2207, 2225}
\begin {gather*} -x+4 e^x+e^x \left (-4 x+14+\log ^2(2)-8 \log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^x \left (14-4 x-8 \log (2)+\log ^2(2)\right ) \, dx\\ &=-x+e^x \left (14-4 x-8 \log (2)+\log ^2(2)\right )+4 \int e^x \, dx\\ &=4 e^x-x+e^x \left (14-4 x-8 \log (2)+\log ^2(2)\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 21, normalized size = 0.62 \begin {gather*} -x+e^x \left (18-4 x-8 \log (2)+\log ^2(2)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.04, size = 27, normalized size = 0.79
method | result | size |
risch | \(\left (\ln \left (2\right )^{2}-8 \ln \left (2\right )-4 x +18\right ) {\mathrm e}^{x}-x\) | \(21\) |
norman | \(\left (18+\ln \left (2\right )^{2}-8 \ln \left (2\right )\right ) {\mathrm e}^{x}-x -4 \,{\mathrm e}^{x} x\) | \(23\) |
default | \(-x +\ln \left (2\right )^{2} {\mathrm e}^{x}-4 \,{\mathrm e}^{x} x +18 \,{\mathrm e}^{x}-8 \,{\mathrm e}^{x} \ln \left (2\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 28, normalized size = 0.82 \begin {gather*} e^{x} \log \left (2\right )^{2} - 4 \, {\left (x - 1\right )} e^{x} - 8 \, e^{x} \log \left (2\right ) - x + 14 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 20, normalized size = 0.59 \begin {gather*} {\left (\log \left (2\right )^{2} - 4 \, x - 8 \, \log \left (2\right ) + 18\right )} e^{x} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 19, normalized size = 0.56 \begin {gather*} - x + \left (- 4 x - 8 \log {\left (2 \right )} + \log {\left (2 \right )}^{2} + 18\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 20, normalized size = 0.59 \begin {gather*} {\left (\log \left (2\right )^{2} - 4 \, x - 8 \, \log \left (2\right ) + 18\right )} e^{x} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.72, size = 22, normalized size = 0.65 \begin {gather*} {\mathrm {e}}^x\,\left ({\ln \left (2\right )}^2-\ln \left (256\right )+18\right )-x-4\,x\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________