Optimal. Leaf size=33 \[ \frac {3}{x-e^x x+\frac {1}{2} \left (-e^x+\frac {x^2}{(49-x)^2}\right )} \]
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Rubi [F]
time = 4.68, 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 {-69177612+5618340 x-172284 x^2+2352 x^3-12 x^4+e^x \left (103766418+60706884 x-5387844 x^2+169344 x^3-2334 x^4+12 x^5\right )}{23059204 x^2-1872780 x^3+57233 x^4-780 x^5+4 x^6+e^x \left (-23059204 x-44240826 x^2+3697736 x^3-114074 x^4+1560 x^5-8 x^6\right )+e^{2 x} \left (5764801+22588608 x+21191226 x^2-1824956 x^3+56841 x^4-780 x^5+4 x^6\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 (49-x) \left (-e^x (-49+x)^3 (3+2 x)+2 \left (-117649+7154 x-147 x^2+x^3\right )\right )}{\left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx\\ &=6 \int \frac {(49-x) \left (-e^x (-49+x)^3 (3+2 x)+2 \left (-117649+7154 x-147 x^2+x^3\right )\right )}{\left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx\\ &=6 \int \left (\frac {(-49+x)^2 (3+2 x)}{(1+2 x) \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )}+\frac {-11529602+12465992 x+22086897 x^2-1848476 x^3+57037 x^4-780 x^5+4 x^6}{(1+2 x) \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2}\right ) \, dx\\ &=6 \int \frac {(-49+x)^2 (3+2 x)}{(1+2 x) \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )} \, dx+6 \int \frac {-11529602+12465992 x+22086897 x^2-1848476 x^3+57037 x^4-780 x^5+4 x^6}{(1+2 x) \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2} \, dx\\ &=6 \int \frac {-11529602+12465992 x+22086897 x^2-1848476 x^3+57037 x^4-780 x^5+4 x^6}{(1+2 x) \left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx+6 \int \left (\frac {4605}{2 \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )}-\frac {97 x}{2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3}+\frac {x^2}{2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3}+\frac {9801}{2 (1+2 x) \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )}\right ) \, dx\\ &=6 \int \frac {x^2}{2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3} \, dx+6 \int \left (\frac {476623}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2}+\frac {11512746 x}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2}-\frac {938595 x^2}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2}+\frac {28714 x^3}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2}-\frac {391 x^4}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2}+\frac {2 x^5}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2}-\frac {12006225}{(1+2 x) \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2}\right ) \, dx-582 \int \frac {x}{2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3} \, dx+13815 \int \frac {1}{2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3} \, dx+29403 \int \frac {1}{(1+2 x) \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )} \, dx\\ &=6 \int \frac {x^2}{e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )} \, dx+12 \int \frac {x^5}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2} \, dx-582 \int \frac {x}{e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )} \, dx-2346 \int \frac {x^4}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2} \, dx+13815 \int \frac {1}{e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )} \, dx+29403 \int \frac {1}{(1+2 x) \left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )} \, dx+172284 \int \frac {x^3}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2} \, dx+2859738 \int \frac {1}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2} \, dx-5631570 \int \frac {x^2}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2} \, dx+69076476 \int \frac {x}{\left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2} \, dx-72037350 \int \frac {1}{(1+2 x) \left (2401 e^x-4802 x+4704 e^x x+195 x^2-195 e^x x^2-2 x^3+2 e^x x^3\right )^2} \, dx\\ &=6 \int \frac {x^2}{e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )} \, dx+12 \int \frac {x^5}{\left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx-582 \int \frac {x}{e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )} \, dx-2346 \int \frac {x^4}{\left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx+13815 \int \frac {1}{e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )} \, dx+29403 \int \frac {1}{(1+2 x) \left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )} \, dx+172284 \int \frac {x^3}{\left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx+2859738 \int \frac {1}{\left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx-5631570 \int \frac {x^2}{\left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx+69076476 \int \frac {x}{\left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx-72037350 \int \frac {1}{(1+2 x) \left (e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 4.09, size = 36, normalized size = 1.09 \begin {gather*} -\frac {6 (-49+x)^2}{e^x (-49+x)^2 (1+2 x)+x \left (-4802+195 x-2 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.30, size = 47, normalized size = 1.42
method | result | size |
risch | \(-\frac {6 \left (x -49\right )^{2}}{2 \,{\mathrm e}^{x} x^{3}-195 \,{\mathrm e}^{x} x^{2}-2 x^{3}+4704 \,{\mathrm e}^{x} x +195 x^{2}+2401 \,{\mathrm e}^{x}-4802 x}\) | \(47\) |
norman | \(\frac {-6 x^{2}+588 x -14406}{2 \,{\mathrm e}^{x} x^{3}-195 \,{\mathrm e}^{x} x^{2}-2 x^{3}+4704 \,{\mathrm e}^{x} x +195 x^{2}+2401 \,{\mathrm e}^{x}-4802 x}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.38, size = 45, normalized size = 1.36 \begin {gather*} \frac {6 \, {\left (x^{2} - 98 \, x + 2401\right )}}{2 \, x^{3} - 195 \, x^{2} - {\left (2 \, x^{3} - 195 \, x^{2} + 4704 \, x + 2401\right )} e^{x} + 4802 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 45, normalized size = 1.36 \begin {gather*} \frac {6 \, {\left (x^{2} - 98 \, x + 2401\right )}}{2 \, x^{3} - 195 \, x^{2} - {\left (2 \, x^{3} - 195 \, x^{2} + 4704 \, x + 2401\right )} e^{x} + 4802 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.20, size = 41, normalized size = 1.24 \begin {gather*} \frac {- 6 x^{2} + 588 x - 14406}{- 2 x^{3} + 195 x^{2} - 4802 x + \left (2 x^{3} - 195 x^{2} + 4704 x + 2401\right ) e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 49, normalized size = 1.48 \begin {gather*} -\frac {6 \, {\left (x^{2} - 98 \, x + 2401\right )}}{2 \, x^{3} e^{x} - 2 \, x^{3} - 195 \, x^{2} e^{x} + 195 \, x^{2} + 4704 \, x e^{x} - 4802 \, x + 2401 \, e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {5618340\,x+{\mathrm {e}}^x\,\left (12\,x^5-2334\,x^4+169344\,x^3-5387844\,x^2+60706884\,x+103766418\right )-172284\,x^2+2352\,x^3-12\,x^4-69177612}{23059204\,x^2-{\mathrm {e}}^x\,\left (8\,x^6-1560\,x^5+114074\,x^4-3697736\,x^3+44240826\,x^2+23059204\,x\right )-1872780\,x^3+57233\,x^4-780\,x^5+4\,x^6+{\mathrm {e}}^{2\,x}\,\left (4\,x^6-780\,x^5+56841\,x^4-1824956\,x^3+21191226\,x^2+22588608\,x+5764801\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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