Optimal. Leaf size=23 \[ \frac {2 x^2}{x+\left (7-e^x+\frac {3}{x}\right ) x} \]
________________________________________________________________________________________
Rubi [F] time = 0.91, 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 {12 x+16 x^2+e^x \left (-2 x^2+2 x^3\right )}{9+48 x+64 x^2+e^{2 x} x^2+e^x \left (-6 x-16 x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \left (6-\left (-8+e^x\right ) x+e^x x^2\right )}{\left (3-\left (-8+e^x\right ) x\right )^2} \, dx\\ &=2 \int \frac {x \left (6-\left (-8+e^x\right ) x+e^x x^2\right )}{\left (3-\left (-8+e^x\right ) x\right )^2} \, dx\\ &=2 \int \left (\frac {(-1+x) x}{-3-8 x+e^x x}+\frac {x \left (3+3 x+8 x^2\right )}{\left (-3-8 x+e^x x\right )^2}\right ) \, dx\\ &=2 \int \frac {(-1+x) x}{-3-8 x+e^x x} \, dx+2 \int \frac {x \left (3+3 x+8 x^2\right )}{\left (-3-8 x+e^x x\right )^2} \, dx\\ &=2 \int \left (\frac {3 x}{\left (-3-8 x+e^x x\right )^2}+\frac {3 x^2}{\left (-3-8 x+e^x x\right )^2}+\frac {8 x^3}{\left (-3-8 x+e^x x\right )^2}\right ) \, dx+2 \int \left (-\frac {x}{-3-8 x+e^x x}+\frac {x^2}{-3-8 x+e^x x}\right ) \, dx\\ &=-\left (2 \int \frac {x}{-3-8 x+e^x x} \, dx\right )+2 \int \frac {x^2}{-3-8 x+e^x x} \, dx+6 \int \frac {x}{\left (-3-8 x+e^x x\right )^2} \, dx+6 \int \frac {x^2}{\left (-3-8 x+e^x x\right )^2} \, dx+16 \int \frac {x^3}{\left (-3-8 x+e^x x\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.21, size = 17, normalized size = 0.74 \begin {gather*} -\frac {2 x^2}{-3-8 x+e^x x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.02, size = 16, normalized size = 0.70 \begin {gather*} -\frac {2 \, x^{2}}{x e^{x} - 8 \, x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 16, normalized size = 0.70 \begin {gather*} -\frac {2 \, x^{2}}{x e^{x} - 8 \, x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 17, normalized size = 0.74
method | result | size |
norman | \(-\frac {2 x^{2}}{{\mathrm e}^{x} x -8 x -3}\) | \(17\) |
risch | \(-\frac {2 x^{2}}{{\mathrm e}^{x} x -8 x -3}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 16, normalized size = 0.70 \begin {gather*} -\frac {2 \, x^{2}}{x e^{x} - 8 \, x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.14, size = 17, normalized size = 0.74 \begin {gather*} \frac {2\,x^2}{8\,x-x\,{\mathrm {e}}^x+3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 15, normalized size = 0.65 \begin {gather*} - \frac {2 x^{2}}{x e^{x} - 8 x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________