Optimal. Leaf size=28 \[ 45 \left (e^x+\frac {5 \left (2+\frac {9}{\left (-2+\frac {2+x}{4}\right )^2}\right )}{3+x}\right ) \]
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Rubi [A] time = 0.19, antiderivative size = 31, normalized size of antiderivative = 1.11, number of steps used = 6, number of rules used = 4, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {6688, 12, 2194, 1620} \begin {gather*} 45 e^x+\frac {850}{x+3}+\frac {400}{6-x}+\frac {3600}{(6-x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1620
Rule 2194
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 45 \left (e^x-\frac {10 \left (-216+324 x-18 x^2+x^3\right )}{(-6+x)^3 (3+x)^2}\right ) \, dx\\ &=45 \int \left (e^x-\frac {10 \left (-216+324 x-18 x^2+x^3\right )}{(-6+x)^3 (3+x)^2}\right ) \, dx\\ &=45 \int e^x \, dx-450 \int \frac {-216+324 x-18 x^2+x^3}{(-6+x)^3 (3+x)^2} \, dx\\ &=45 e^x-450 \int \left (\frac {16}{(-6+x)^3}-\frac {8}{9 (-6+x)^2}+\frac {17}{9 (3+x)^2}\right ) \, dx\\ &=45 e^x+\frac {3600}{(6-x)^2}+\frac {400}{6-x}+\frac {850}{3+x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 31, normalized size = 1.11 \begin {gather*} 45 \left (e^x+\frac {80}{(-6+x)^2}-\frac {80}{9 (-6+x)}+\frac {170}{9 (3+x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 37, normalized size = 1.32 \begin {gather*} \frac {45 \, {\left (10 \, x^{2} + {\left (x^{3} - 9 \, x^{2} + 108\right )} e^{x} - 120 \, x + 1080\right )}}{x^{3} - 9 \, x^{2} + 108} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 41, normalized size = 1.46 \begin {gather*} \frac {45 \, {\left (x^{3} e^{x} - 9 \, x^{2} e^{x} + 10 \, x^{2} - 120 \, x + 108 \, e^{x} + 1080\right )}}{x^{3} - 9 \, x^{2} + 108} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 27, normalized size = 0.96
method | result | size |
default | \(\frac {3600}{\left (x -6\right )^{2}}-\frac {400}{x -6}+\frac {850}{3+x}+45 \,{\mathrm e}^{x}\) | \(27\) |
risch | \(\frac {450 x^{2}-5400 x +48600}{x^{3}-9 x^{2}+108}+45 \,{\mathrm e}^{x}\) | \(29\) |
norman | \(\frac {450 x^{2}-5400 x -405 \,{\mathrm e}^{x} x^{2}+45 \,{\mathrm e}^{x} x^{3}+4860 \,{\mathrm e}^{x}+48600}{\left (3+x \right ) \left (x -6\right )^{2}}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.48, size = 89, normalized size = 3.18 \begin {gather*} \frac {50 \, {\left (7 \, x^{2} - 12 \, x - 72\right )}}{x^{3} - 9 \, x^{2} + 108} + \frac {200 \, {\left (2 \, x^{2} - 15 \, x - 9\right )}}{x^{3} - 9 \, x^{2} + 108} - \frac {300 \, {\left (x^{2} + 6 \, x - 18\right )}}{x^{3} - 9 \, x^{2} + 108} + \frac {48600}{x^{3} - 9 \, x^{2} + 108} + 45 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.59, size = 26, normalized size = 0.93 \begin {gather*} 45\,{\mathrm {e}}^x+\frac {450\,x^2-5400\,x+48600}{\left (x+3\right )\,{\left (x-6\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 24, normalized size = 0.86 \begin {gather*} - \frac {- 450 x^{2} + 5400 x - 48600}{x^{3} - 9 x^{2} + 108} + 45 e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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