Optimal. Leaf size=26 \[ \frac {1}{3} e^{-15 e^{-x} (5-x) x-2 x^2} x \]
________________________________________________________________________________________
Rubi [F] time = 1.26, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{3} e^{-x-e^{-x} \left (75 x-15 x^2+2 e^x x^2\right )} \left (-75 x+105 x^2-15 x^3+e^x \left (1-4 x^2\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{-x-e^{-x} \left (75 x-15 x^2+2 e^x x^2\right )} \left (-75 x+105 x^2-15 x^3+e^x \left (1-4 x^2\right )\right ) \, dx\\ &=\frac {1}{3} \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} \left (-75 x+105 x^2-15 x^3+e^x \left (1-4 x^2\right )\right ) \, dx\\ &=\frac {1}{3} \int \left (-75 e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x+105 e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^2-15 e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^3-e^{x-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} \left (-1+4 x^2\right )\right ) \, dx\\ &=-\left (\frac {1}{3} \int e^{x-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} \left (-1+4 x^2\right ) \, dx\right )-5 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^3 \, dx-25 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x \, dx+35 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^2 \, dx\\ &=-\left (\frac {1}{3} \int e^{-e^{-x} x \left (75-15 x+2 e^x x\right )} \left (-1+4 x^2\right ) \, dx\right )-5 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^3 \, dx-25 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x \, dx+35 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^2 \, dx\\ &=-\left (\frac {1}{3} \int \left (-e^{-e^{-x} x \left (75-15 x+2 e^x x\right )}+4 e^{-e^{-x} x \left (75-15 x+2 e^x x\right )} x^2\right ) \, dx\right )-5 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^3 \, dx-25 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x \, dx+35 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^2 \, dx\\ &=\frac {1}{3} \int e^{-e^{-x} x \left (75-15 x+2 e^x x\right )} \, dx-\frac {4}{3} \int e^{-e^{-x} x \left (75-15 x+2 e^x x\right )} x^2 \, dx-5 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^3 \, dx-25 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x \, dx+35 \int e^{-e^{-x} x \left (75+e^x-15 x+2 e^x x\right )} x^2 \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.32, size = 24, normalized size = 0.92 \begin {gather*} \frac {1}{3} e^{15 e^{-x} (-5+x) x-2 x^2} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.46, size = 31, normalized size = 1.19 \begin {gather*} \frac {1}{3} \, x e^{\left ({\left (15 \, x^{2} - {\left (2 \, x^{2} + x\right )} e^{x} - 75 \, x\right )} e^{\left (-x\right )} + x\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 -\frac {1}{3} \, {\left (15 \, x^{3} - 105 \, x^{2} + {\left (4 \, x^{2} - 1\right )} e^{x} + 75 \, x\right )} e^{\left (-{\left (2 \, x^{2} e^{x} - 15 \, x^{2} + 75 \, x\right )} e^{\left (-x\right )} - x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 22, normalized size = 0.85
method | result | size |
risch | \(\frac {x \,{\mathrm e}^{-x \left (2 \,{\mathrm e}^{x} x -15 x +75\right ) {\mathrm e}^{-x}}}{3}\) | \(22\) |
norman | \(\frac {x \,{\mathrm e}^{-\left (2 \,{\mathrm e}^{x} x^{2}-15 x^{2}+75 x \right ) {\mathrm e}^{-x}}}{3}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.48, size = 26, normalized size = 1.00 \begin {gather*} \frac {1}{3} \, x e^{\left (15 \, x^{2} e^{\left (-x\right )} - 2 \, x^{2} - 75 \, x e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.30, size = 27, normalized size = 1.04 \begin {gather*} \frac {x\,{\mathrm {e}}^{-75\,x\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{-2\,x^2}\,{\mathrm {e}}^{15\,x^2\,{\mathrm {e}}^{-x}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.24, size = 24, normalized size = 0.92 \begin {gather*} \frac {x e^{- \left (2 x^{2} e^{x} - 15 x^{2} + 75 x\right ) e^{- x}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________