Optimal. Leaf size=26 \[ -e^{x-\frac {x}{7-x}}+\frac {4}{x^2}-\log (18) \]
________________________________________________________________________________________
Rubi [A] time = 0.77, antiderivative size = 24, normalized size of antiderivative = 0.92, number of steps used = 5, number of rules used = 4, integrand size = 59, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.068, Rules used = {1594, 27, 6742, 6706} \begin {gather*} \frac {4}{x^2}-e^{\frac {(6-x) x}{7-x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 1594
Rule 6706
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-392+112 x-8 x^2+e^{\frac {-6 x+x^2}{-7+x}} \left (-42 x^3+14 x^4-x^5\right )}{x^3 \left (49-14 x+x^2\right )} \, dx\\ &=\int \frac {-392+112 x-8 x^2+e^{\frac {-6 x+x^2}{-7+x}} \left (-42 x^3+14 x^4-x^5\right )}{(-7+x)^2 x^3} \, dx\\ &=\int \left (-\frac {8}{x^3}-\frac {e^{\frac {(-6+x) x}{-7+x}} \left (42-14 x+x^2\right )}{(-7+x)^2}\right ) \, dx\\ &=\frac {4}{x^2}-\int \frac {e^{\frac {(-6+x) x}{-7+x}} \left (42-14 x+x^2\right )}{(-7+x)^2} \, dx\\ &=-e^{\frac {(6-x) x}{7-x}}+\frac {4}{x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.14, size = 20, normalized size = 0.77 \begin {gather*} -e^{1+\frac {7}{-7+x}+x}+\frac {4}{x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.94, size = 25, normalized size = 0.96 \begin {gather*} -\frac {x^{2} e^{\left (\frac {x^{2} - 6 \, x}{x - 7}\right )} - 4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.29, size = 25, normalized size = 0.96 \begin {gather*} -\frac {x^{2} e^{\left (\frac {x^{2} - 6 \, x}{x - 7}\right )} - 4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.12, size = 20, normalized size = 0.77
method | result | size |
risch | \(\frac {4}{x^{2}}-{\mathrm e}^{\frac {x \left (x -6\right )}{x -7}}\) | \(20\) |
norman | \(\frac {-28+4 x +7 x^{2} {\mathrm e}^{\frac {x^{2}-6 x}{x -7}}-x^{3} {\mathrm e}^{\frac {x^{2}-6 x}{x -7}}}{x^{2} \left (x -7\right )}\) | \(53\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.61, size = 60, normalized size = 2.31 \begin {gather*} \frac {4 \, {\left (6 \, x^{2} - 21 \, x - 49\right )}}{7 \, {\left (x^{3} - 7 \, x^{2}\right )}} - \frac {16 \, {\left (2 \, x - 7\right )}}{7 \, {\left (x^{2} - 7 \, x\right )}} + \frac {8}{7 \, {\left (x - 7\right )}} - e^{\left (x + \frac {7}{x - 7} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.23, size = 27, normalized size = 1.04 \begin {gather*} \frac {4}{x^2}-{\mathrm {e}}^{-\frac {6\,x}{x-7}}\,{\mathrm {e}}^{\frac {x^2}{x-7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.18, size = 15, normalized size = 0.58 \begin {gather*} - e^{\frac {x^{2} - 6 x}{x - 7}} + \frac {4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________