Optimal. Leaf size=34 \[ -x+\left (5 e^x+5 \left (x+e^{\frac {e^{2+x}}{5}} x-x^2\right )\right )^2 \]
________________________________________________________________________________________
Rubi [B] time = 0.12, antiderivative size = 83, normalized size of antiderivative = 2.44, number of steps used = 12, number of rules used = 4, integrand size = 115, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {2194, 2196, 2176, 2288} \begin {gather*} 25 x^4-50 x^3+25 e^{\frac {2 e^{x+2}}{5}} x^2-50 e^x x^2+25 x^2+50 e^{\frac {e^{x+2}}{5}} \left (-x^3+x^2+e^x x\right )+50 e^x x-x+25 e^{2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2176
Rule 2194
Rule 2196
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+25 x^2-50 x^3+25 x^4+50 \int e^{2 x} \, dx+\int e^x \left (50-50 x-50 x^2\right ) \, dx+\int e^{\frac {2 e^{2+x}}{5}} \left (50 x+10 e^{2+x} x^2\right ) \, dx+\int e^{\frac {e^{2+x}}{5}} \left (100 x-150 x^2+e^x (50+50 x)+e^{2+x} \left (10 e^x x+10 x^2-10 x^3\right )\right ) \, dx\\ &=25 e^{2 x}-x+25 x^2+25 e^{\frac {2 e^{2+x}}{5}} x^2-50 x^3+25 x^4+50 e^{\frac {e^{2+x}}{5}} \left (e^x x+x^2-x^3\right )+\int \left (50 e^x-50 e^x x-50 e^x x^2\right ) \, dx\\ &=25 e^{2 x}-x+25 x^2+25 e^{\frac {2 e^{2+x}}{5}} x^2-50 x^3+25 x^4+50 e^{\frac {e^{2+x}}{5}} \left (e^x x+x^2-x^3\right )+50 \int e^x \, dx-50 \int e^x x \, dx-50 \int e^x x^2 \, dx\\ &=50 e^x+25 e^{2 x}-x-50 e^x x+25 x^2+25 e^{\frac {2 e^{2+x}}{5}} x^2-50 e^x x^2-50 x^3+25 x^4+50 e^{\frac {e^{2+x}}{5}} \left (e^x x+x^2-x^3\right )+50 \int e^x \, dx+100 \int e^x x \, dx\\ &=100 e^x+25 e^{2 x}-x+50 e^x x+25 x^2+25 e^{\frac {2 e^{2+x}}{5}} x^2-50 e^x x^2-50 x^3+25 x^4+50 e^{\frac {e^{2+x}}{5}} \left (e^x x+x^2-x^3\right )-100 \int e^x \, dx\\ &=25 e^{2 x}-x+50 e^x x+25 x^2+25 e^{\frac {2 e^{2+x}}{5}} x^2-50 e^x x^2-50 x^3+25 x^4+50 e^{\frac {e^{2+x}}{5}} \left (e^x x+x^2-x^3\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] time = 0.09, size = 78, normalized size = 2.29 \begin {gather*} 25 e^{2 x}-x+25 x^2+25 e^{\frac {2 e^{2+x}}{5}} x^2-50 x^3+25 x^4+50 e^{\frac {e^{2+x}}{5}} x \left (e^x+x-x^2\right )-50 e^x \left (-x+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.78, size = 90, normalized size = 2.65 \begin {gather*} {\left (25 \, x^{2} e^{\left (\frac {2}{5} \, e^{\left (x + 2\right )} + 4\right )} + {\left (25 \, x^{4} - 50 \, x^{3} + 25 \, x^{2} - x\right )} e^{4} - 50 \, {\left (x^{2} - x\right )} e^{\left (x + 4\right )} - 50 \, {\left ({\left (x^{3} - x^{2}\right )} e^{4} - x e^{\left (x + 4\right )}\right )} e^{\left (\frac {1}{5} \, e^{\left (x + 2\right )}\right )} + 25 \, e^{\left (2 \, x + 4\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 100 \, x^{3} - 150 \, x^{2} - 50 \, {\left (x^{2} + x - 1\right )} e^{x} + 10 \, {\left (x^{2} e^{\left (x + 2\right )} + 5 \, x\right )} e^{\left (\frac {2}{5} \, e^{\left (x + 2\right )}\right )} - 10 \, {\left (15 \, x^{2} + {\left (x^{3} - x^{2} - x e^{x}\right )} e^{\left (x + 2\right )} - 5 \, {\left (x + 1\right )} e^{x} - 10 \, x\right )} e^{\left (\frac {1}{5} \, e^{\left (x + 2\right )}\right )} + 50 \, x + 50 \, e^{\left (2 \, x\right )} - 1\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.14, size = 71, normalized size = 2.09
method | result | size |
risch | \(25 x^{2} {\mathrm e}^{\frac {2 \,{\mathrm e}^{2+x}}{5}}-50 x \left (x^{2}-x -{\mathrm e}^{x}\right ) {\mathrm e}^{\frac {{\mathrm e}^{2+x}}{5}}+25 \,{\mathrm e}^{2 x}+\left (-50 x^{2}+50 x \right ) {\mathrm e}^{x}+25 x^{4}-50 x^{3}+25 x^{2}-x\) | \(71\) |
default | \(-x +25 x^{2} {\mathrm e}^{\frac {2 \,{\mathrm e}^{2+x}}{5}}-50 x^{3} {\mathrm e}^{\frac {{\mathrm e}^{2} {\mathrm e}^{x}}{5}}+50 \,{\mathrm e}^{\frac {{\mathrm e}^{2} {\mathrm e}^{x}}{5}} x^{2}+50 \,{\mathrm e}^{\frac {{\mathrm e}^{2} {\mathrm e}^{x}}{5}} x \,{\mathrm e}^{x}+50 \,{\mathrm e}^{x} x -50 \,{\mathrm e}^{x} x^{2}+25 x^{2}-50 x^{3}+25 x^{4}+25 \,{\mathrm e}^{2 x}\) | \(88\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.40, size = 71, normalized size = 2.09 \begin {gather*} 25 \, x^{4} - 50 \, x^{3} + 25 \, x^{2} e^{\left (\frac {2}{5} \, e^{\left (x + 2\right )}\right )} + 25 \, x^{2} - 50 \, {\left (x^{2} - x\right )} e^{x} - 50 \, {\left (x^{3} - x^{2} - x e^{x}\right )} e^{\left (\frac {1}{5} \, e^{\left (x + 2\right )}\right )} - x + 25 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.84, size = 85, normalized size = 2.50 \begin {gather*} 25\,{\mathrm {e}}^{2\,x}-x-50\,x^2\,{\mathrm {e}}^x+50\,x^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^2\,{\mathrm {e}}^x}{5}}+25\,x^2\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^2\,{\mathrm {e}}^x}{5}}-50\,x^3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^2\,{\mathrm {e}}^x}{5}}+50\,x\,{\mathrm {e}}^x+50\,x\,{\mathrm {e}}^{x+\frac {{\mathrm {e}}^2\,{\mathrm {e}}^x}{5}}+25\,x^2-50\,x^3+25\,x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.32, size = 78, normalized size = 2.29 \begin {gather*} 25 x^{4} - 50 x^{3} + 25 x^{2} e^{\frac {2 e^{2} e^{x}}{5}} + 25 x^{2} - x + \left (- 50 x^{2} + 50 x\right ) e^{x} + \left (- 50 x^{3} + 50 x^{2} + 50 x e^{x}\right ) e^{\frac {e^{2} e^{x}}{5}} + 25 e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________