Optimal. Leaf size=29 \[ -x+e^{2 x} \left (2+2^{2/5} e^{2 e^{12} x^4}+x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.09, antiderivative size = 48, normalized size of antiderivative = 1.66, number of steps
used = 4, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2207, 2225,
6838} \begin {gather*} e^{\frac {2}{5} \left (5 e^{12} x^4+\log (2)\right )+2 x}-x-\frac {e^{2 x}}{2}+\frac {1}{2} e^{2 x} (2 x+5) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2207
Rule 2225
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^{2 x} (5+2 x) \, dx+\int e^{2 x+\frac {2}{5} \left (5 e^{12} x^4+\log (2)\right )} \left (2+8 e^{12} x^3\right ) \, dx\\ &=e^{2 x+\frac {2}{5} \left (5 e^{12} x^4+\log (2)\right )}-x+\frac {1}{2} e^{2 x} (5+2 x)-\int e^{2 x} \, dx\\ &=-\frac {e^{2 x}}{2}+e^{2 x+\frac {2}{5} \left (5 e^{12} x^4+\log (2)\right )}-x+\frac {1}{2} e^{2 x} (5+2 x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.09, size = 32, normalized size = 1.10 \begin {gather*} 2^{2/5} e^{2 \left (x+e^{12} x^4\right )}-x+e^{2 x} (2+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.73, size = 33, normalized size = 1.14
method | result | size |
risch | \(2^{\frac {2}{5}} {\mathrm e}^{2 x \left ({\mathrm e}^{12} x^{3}+1\right )}+\left (2+x \right ) {\mathrm e}^{2 x}-x\) | \(29\) |
default | \(-x +x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x +\frac {2 \ln \left (2\right )}{5}+2 \,{\mathrm e}^{12} x^{4}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 37, normalized size = 1.28 \begin {gather*} \frac {1}{2} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} - x + e^{\left (2 \, x^{4} e^{12} + 2 \, x + \frac {2}{5} \, \log \left (2\right )\right )} + \frac {5}{2} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 28, normalized size = 0.97 \begin {gather*} {\left (x + 2\right )} e^{\left (2 \, x\right )} - x + e^{\left (2 \, x^{4} e^{12} + 2 \, x + \frac {2}{5} \, \log \left (2\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.25, size = 29, normalized size = 1.00 \begin {gather*} - x + \left (x + 2\right ) e^{2 x} + 2^{\frac {2}{5}} e^{2 x} e^{2 x^{4} e^{12}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 28, normalized size = 0.97 \begin {gather*} {\left (x + 2\right )} e^{\left (2 \, x\right )} + 2^{\frac {2}{5}} e^{\left (2 \, x^{4} e^{12} + 2 \, x\right )} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.18, size = 32, normalized size = 1.10 \begin {gather*} 2\,{\mathrm {e}}^{2\,x}-x+x\,{\mathrm {e}}^{2\,x}+2^{2/5}\,{\mathrm {e}}^{2\,{\mathrm {e}}^{12}\,x^4+2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________