Optimal. Leaf size=28 \[ \left (9+\frac {45 \left (1-\frac {e^5}{x}\right )}{4 (3-x)}-x\right ) x \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 27, normalized size of antiderivative = 0.96, number of steps used = 4, number of rules used = 3, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {27, 12, 1850} \begin {gather*} -x^2+9 x+\frac {45 \left (3-e^5\right )}{4 (3-x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 27
Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {459-45 e^5-288 x+84 x^2-8 x^3}{4 (-3+x)^2} \, dx\\ &=\frac {1}{4} \int \frac {459-45 e^5-288 x+84 x^2-8 x^3}{(-3+x)^2} \, dx\\ &=\frac {1}{4} \int \left (36-\frac {45 \left (-3+e^5\right )}{(-3+x)^2}-8 x\right ) \, dx\\ &=\frac {45 \left (3-e^5\right )}{4 (3-x)}+9 x-x^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 29, normalized size = 1.04 \begin {gather*} \frac {1}{4} \left (\frac {45 \left (-3+e^5\right )}{-3+x}+12 (-3+x)-4 (-3+x)^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.85, size = 26, normalized size = 0.93 \begin {gather*} -\frac {4 \, x^{3} - 48 \, x^{2} + 108 \, x - 45 \, e^{5} + 135}{4 \, {\left (x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.35, size = 20, normalized size = 0.71 \begin {gather*} -x^{2} + 9 \, x + \frac {45 \, {\left (e^{5} - 3\right )}}{4 \, {\left (x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.40, size = 23, normalized size = 0.82
method | result | size |
default | \(9 x -x^{2}-\frac {135-45 \,{\mathrm e}^{5}}{4 \left (x -3\right )}\) | \(23\) |
norman | \(\frac {12 x^{2}-x^{3}-\frac {459}{4}+\frac {45 \,{\mathrm e}^{5}}{4}}{x -3}\) | \(23\) |
gosper | \(\frac {-4 x^{3}+48 x^{2}+45 \,{\mathrm e}^{5}-459}{4 x -12}\) | \(24\) |
risch | \(-x^{2}+9 x -\frac {135}{4 \left (x -3\right )}+\frac {45 \,{\mathrm e}^{5}}{4 \left (x -3\right )}\) | \(26\) |
meijerg | \(-\frac {45 x}{4 \left (1-\frac {x}{3}\right )}-\frac {5 \,{\mathrm e}^{5} x}{4 \left (1-\frac {x}{3}\right )}-\frac {3 x \left (-\frac {2}{9} x^{2}-2 x +12\right )}{2 \left (1-\frac {x}{3}\right )}+\frac {7 x \left (-x +6\right )}{1-\frac {x}{3}}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 20, normalized size = 0.71 \begin {gather*} -x^{2} + 9 \, x + \frac {45 \, {\left (e^{5} - 3\right )}}{4 \, {\left (x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 23, normalized size = 0.82 \begin {gather*} 9\,x+\frac {45\,{\mathrm {e}}^5-135}{4\,x-12}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 17, normalized size = 0.61 \begin {gather*} - x^{2} + 9 x - \frac {135 - 45 e^{5}}{4 x - 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________