Optimal. Leaf size=28 \[ -4-x+4 \left (16 e^{25}+e^{\frac {1}{3-x}}+4 e^x+x\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.23, antiderivative size = 20, normalized size of antiderivative = 0.71, number of steps used = 9, number of rules used = 5, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.109, Rules used = {27, 6742, 2194, 2209, 43} \begin {gather*} 3 x+16 e^x+4 e^{\frac {1}{3-x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 43
Rule 2194
Rule 2209
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {27+4 e^{-\frac {1}{-3+x}}-18 x+3 x^2+e^x \left (144-96 x+16 x^2\right )}{(-3+x)^2} \, dx\\ &=\int \left (16 e^x+\frac {27}{(-3+x)^2}+\frac {4 e^{\frac {1}{3-x}}}{(-3+x)^2}-\frac {18 x}{(-3+x)^2}+\frac {3 x^2}{(-3+x)^2}\right ) \, dx\\ &=\frac {27}{3-x}+3 \int \frac {x^2}{(-3+x)^2} \, dx+4 \int \frac {e^{\frac {1}{3-x}}}{(-3+x)^2} \, dx+16 \int e^x \, dx-18 \int \frac {x}{(-3+x)^2} \, dx\\ &=4 e^{\frac {1}{3-x}}+16 e^x+\frac {27}{3-x}+3 \int \left (1+\frac {9}{(-3+x)^2}+\frac {6}{-3+x}\right ) \, dx-18 \int \left (\frac {3}{(-3+x)^2}+\frac {1}{-3+x}\right ) \, dx\\ &=4 e^{\frac {1}{3-x}}+16 e^x+3 x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.09, size = 20, normalized size = 0.71 \begin {gather*} 4 e^{\frac {1}{3-x}}+16 e^x+3 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 18, normalized size = 0.64 \begin {gather*} 3 \, x + 16 \, e^{x} + 4 \, e^{\left (-\frac {1}{x - 3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.24, size = 18, normalized size = 0.64 \begin {gather*} 3 \, x + 16 \, e^{x} + 4 \, e^{\left (-\frac {1}{x - 3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.57, size = 19, normalized size = 0.68
method | result | size |
default | \(3 x +16 \,{\mathrm e}^{x}+4 \,{\mathrm e}^{-\frac {1}{x -3}}\) | \(19\) |
risch | \(3 x +16 \,{\mathrm e}^{x}+4 \,{\mathrm e}^{-\frac {1}{x -3}}\) | \(19\) |
norman | \(\frac {3 x^{2}+4 x \,{\mathrm e}^{-\frac {1}{x -3}}+16 \,{\mathrm e}^{x} x -48 \,{\mathrm e}^{x}-12 \,{\mathrm e}^{-\frac {1}{x -3}}-27}{x -3}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 3 \, x + \frac {16 \, {\left (x^{2} - 6 \, x\right )} e^{x}}{x^{2} - 6 \, x + 9} - \frac {144 \, e^{3} E_{2}\left (-x + 3\right )}{x - 3} + 4 \, e^{\left (-\frac {1}{x - 3}\right )} - 288 \, \int \frac {e^{x}}{x^{3} - 9 \, x^{2} + 27 \, x - 27}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.19, size = 18, normalized size = 0.64 \begin {gather*} 3\,x+16\,{\mathrm {e}}^x+4\,{\mathrm {e}}^{-\frac {1}{x-3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.20, size = 15, normalized size = 0.54 \begin {gather*} 3 x + 16 e^{x} + 4 e^{- \frac {1}{x - 3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________