Integrand size = 101, antiderivative size = 24 \[ \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx=e^{x+\frac {x}{-\frac {7}{2}+(256-x)^2}}+16 \log (x) \]
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\[ \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx=\int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{x \left (131065-1024 x+2 x^2\right )^2} \, dx \\ & = \int \left (-\frac {4294737920}{\left (131065-1024 x+2 x^2\right )^2}+\frac {274848547600}{x \left (131065-1024 x+2 x^2\right )^2}+\frac {25165376 x}{\left (131065-1024 x+2 x^2\right )^2}-\frac {65536 x^2}{\left (131065-1024 x+2 x^2\right )^2}+\frac {64 x^3}{\left (131065-1024 x+2 x^2\right )^2}+\frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} \left (17178296355-268421120 x+1572832 x^2-4096 x^3+4 x^4\right )}{\left (131065-1024 x+2 x^2\right )^2}\right ) \, dx \\ & = 64 \int \frac {x^3}{\left (131065-1024 x+2 x^2\right )^2} \, dx-65536 \int \frac {x^2}{\left (131065-1024 x+2 x^2\right )^2} \, dx+25165376 \int \frac {x}{\left (131065-1024 x+2 x^2\right )^2} \, dx-4294737920 \int \frac {1}{\left (131065-1024 x+2 x^2\right )^2} \, dx+274848547600 \int \frac {1}{x \left (131065-1024 x+2 x^2\right )^2} \, dx+\int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} \left (17178296355-268421120 x+1572832 x^2-4096 x^3+4 x^4\right )}{\left (131065-1024 x+2 x^2\right )^2} \, dx \\ & = \frac {6291344 (131065-512 x)}{7 \left (131065-1024 x+2 x^2\right )}+\frac {1048520 (131079-512 x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {2147368960 (256-x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {16384 (131065-512 x) x}{7 \left (131065-1024 x+2 x^2\right )}+\frac {16 (131065-512 x) x^2}{7 \left (131065-1024 x+2 x^2\right )}-\frac {8}{7} \int \frac {(524260-1024 x) x}{131065-1024 x+2 x^2} \, dx-\frac {262130}{7} \int \frac {-56+2048 x}{x \left (131065-1024 x+2 x^2\right )} \, dx+2 \left (\frac {2147368960}{7} \int \frac {1}{131065-1024 x+2 x^2} \, dx\right )-\frac {3221168128}{7} \int \frac {1}{131065-1024 x+2 x^2} \, dx+\int \left (e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}-\frac {4 e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} (-131065+512 x)}{\left (131065-1024 x+2 x^2\right )^2}-\frac {2 e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{131065-1024 x+2 x^2}\right ) \, dx \\ & = \frac {4096 x}{7}+\frac {6291344 (131065-512 x)}{7 \left (131065-1024 x+2 x^2\right )}+\frac {1048520 (131079-512 x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {2147368960 (256-x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {16384 (131065-512 x) x}{7 \left (131065-1024 x+2 x^2\right )}+\frac {16 (131065-512 x) x^2}{7 \left (131065-1024 x+2 x^2\right )}-\frac {4}{7} \int \frac {134210560-56 x}{131065-1024 x+2 x^2} \, dx-2 \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{131065-1024 x+2 x^2} \, dx-4 \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} (-131065+512 x)}{\left (131065-1024 x+2 x^2\right )^2} \, dx-\frac {262130}{7} \int \left (-\frac {56}{131065 x}+\frac {16 (16772736+7 x)}{131065 \left (131065-1024 x+2 x^2\right )}\right ) \, dx-2 \left (\frac {4294737920}{7} \text {Subst}\left (\int \frac {1}{56-x^2} \, dx,x,-1024+4 x\right )\right )+\frac {6442336256}{7} \text {Subst}\left (\int \frac {1}{56-x^2} \, dx,x,-1024+4 x\right )+\int e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} \, dx \\ & = \frac {4096 x}{7}+\frac {6291344 (131065-512 x)}{7 \left (131065-1024 x+2 x^2\right )}+\frac {1048520 (131079-512 x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {2147368960 (256-x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {16384 (131065-512 x) x}{7 \left (131065-1024 x+2 x^2\right )}+\frac {16 (131065-512 x) x^2}{7 \left (131065-1024 x+2 x^2\right )}+\frac {536784896}{7} \sqrt {\frac {2}{7}} \text {arctanh}\left (\sqrt {\frac {2}{7}} (256-x)\right )+16 \log (x)-2 \int \left (-\frac {\sqrt {\frac {2}{7}} e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{1024+2 \sqrt {14}-4 x}-\frac {\sqrt {\frac {2}{7}} e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{-1024+2 \sqrt {14}+4 x}\right ) \, dx-4 \int \left (-\frac {131065 e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{\left (131065-1024 x+2 x^2\right )^2}+\frac {512 e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} x}{\left (131065-1024 x+2 x^2\right )^2}\right ) \, dx-\frac {32}{7} \int \frac {16772736+7 x}{131065-1024 x+2 x^2} \, dx+\frac {1}{49} \left (16 \left (49-16774528 \sqrt {14}\right )\right ) \int \frac {1}{-512-\sqrt {14}+2 x} \, dx+\frac {1}{49} \left (16 \left (49+16774528 \sqrt {14}\right )\right ) \int \frac {1}{-512+\sqrt {14}+2 x} \, dx+\int e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} \, dx \\ & = \frac {4096 x}{7}+\frac {6291344 (131065-512 x)}{7 \left (131065-1024 x+2 x^2\right )}+\frac {1048520 (131079-512 x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {2147368960 (256-x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {16384 (131065-512 x) x}{7 \left (131065-1024 x+2 x^2\right )}+\frac {16 (131065-512 x) x^2}{7 \left (131065-1024 x+2 x^2\right )}+\frac {536784896}{7} \sqrt {\frac {2}{7}} \text {arctanh}\left (\sqrt {\frac {2}{7}} (256-x)\right )+\frac {8}{49} \left (49+16774528 \sqrt {14}\right ) \log \left (512-\sqrt {14}-2 x\right )+\frac {8}{49} \left (49-16774528 \sqrt {14}\right ) \log \left (512+\sqrt {14}-2 x\right )+16 \log (x)-2048 \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} x}{\left (131065-1024 x+2 x^2\right )^2} \, dx+524260 \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{\left (131065-1024 x+2 x^2\right )^2} \, dx+\left (2 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{1024+2 \sqrt {14}-4 x} \, dx+\left (2 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{-1024+2 \sqrt {14}+4 x} \, dx-\frac {1}{49} \left (16 \left (49-16774528 \sqrt {14}\right )\right ) \int \frac {1}{-512+\sqrt {14}+2 x} \, dx-\frac {1}{49} \left (16 \left (49+16774528 \sqrt {14}\right )\right ) \int \frac {1}{-512-\sqrt {14}+2 x} \, dx+\int e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} \, dx \\ & = \frac {4096 x}{7}+\frac {6291344 (131065-512 x)}{7 \left (131065-1024 x+2 x^2\right )}+\frac {1048520 (131079-512 x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {2147368960 (256-x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {16384 (131065-512 x) x}{7 \left (131065-1024 x+2 x^2\right )}+\frac {16 (131065-512 x) x^2}{7 \left (131065-1024 x+2 x^2\right )}+\frac {536784896}{7} \sqrt {\frac {2}{7}} \text {arctanh}\left (\sqrt {\frac {2}{7}} (256-x)\right )-\frac {8}{49} \left (49-16774528 \sqrt {14}\right ) \log \left (512-\sqrt {14}-2 x\right )+\frac {8}{49} \left (49+16774528 \sqrt {14}\right ) \log \left (512-\sqrt {14}-2 x\right )+\frac {8}{49} \left (49-16774528 \sqrt {14}\right ) \log \left (512+\sqrt {14}-2 x\right )-\frac {8}{49} \left (49+16774528 \sqrt {14}\right ) \log \left (512+\sqrt {14}-2 x\right )+16 \log (x)-2048 \int \left (\frac {\left (1024+2 \sqrt {14}\right ) e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{14 \left (1024+2 \sqrt {14}-4 x\right )^2}+\frac {128 \sqrt {\frac {2}{7}} e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{7 \left (1024+2 \sqrt {14}-4 x\right )}+\frac {\left (1024-2 \sqrt {14}\right ) e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{14 \left (-1024+2 \sqrt {14}+4 x\right )^2}+\frac {128 \sqrt {\frac {2}{7}} e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{7 \left (-1024+2 \sqrt {14}+4 x\right )}\right ) \, dx+524260 \int \left (\frac {2 e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{7 \left (1024+2 \sqrt {14}-4 x\right )^2}+\frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{7 \sqrt {14} \left (1024+2 \sqrt {14}-4 x\right )}+\frac {2 e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{7 \left (-1024+2 \sqrt {14}+4 x\right )^2}+\frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{7 \sqrt {14} \left (-1024+2 \sqrt {14}+4 x\right )}\right ) \, dx+\left (2 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{1024+2 \sqrt {14}-4 x} \, dx+\left (2 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{-1024+2 \sqrt {14}+4 x} \, dx+\int e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} \, dx \\ & = \frac {4096 x}{7}+\frac {6291344 (131065-512 x)}{7 \left (131065-1024 x+2 x^2\right )}+\frac {1048520 (131079-512 x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {2147368960 (256-x)}{7 \left (131065-1024 x+2 x^2\right )}-\frac {16384 (131065-512 x) x}{7 \left (131065-1024 x+2 x^2\right )}+\frac {16 (131065-512 x) x^2}{7 \left (131065-1024 x+2 x^2\right )}+\frac {536784896}{7} \sqrt {\frac {2}{7}} \text {arctanh}\left (\sqrt {\frac {2}{7}} (256-x)\right )-\frac {8}{49} \left (49-16774528 \sqrt {14}\right ) \log \left (512-\sqrt {14}-2 x\right )+\frac {8}{49} \left (49+16774528 \sqrt {14}\right ) \log \left (512-\sqrt {14}-2 x\right )+\frac {8}{49} \left (49-16774528 \sqrt {14}\right ) \log \left (512+\sqrt {14}-2 x\right )-\frac {8}{49} \left (49+16774528 \sqrt {14}\right ) \log \left (512+\sqrt {14}-2 x\right )+16 \log (x)+\frac {1048520}{7} \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{\left (1024+2 \sqrt {14}-4 x\right )^2} \, dx+\frac {1048520}{7} \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{\left (-1024+2 \sqrt {14}+4 x\right )^2} \, dx+\left (2 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{1024+2 \sqrt {14}-4 x} \, dx+\left (2 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{-1024+2 \sqrt {14}+4 x} \, dx+\frac {1}{7} \left (262130 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{1024+2 \sqrt {14}-4 x} \, dx+\frac {1}{7} \left (262130 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{-1024+2 \sqrt {14}+4 x} \, dx-\frac {1}{7} \left (262144 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{1024+2 \sqrt {14}-4 x} \, dx-\frac {1}{7} \left (262144 \sqrt {\frac {2}{7}}\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{-1024+2 \sqrt {14}+4 x} \, dx-\frac {1}{7} \left (2048 \left (512-\sqrt {14}\right )\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{\left (-1024+2 \sqrt {14}+4 x\right )^2} \, dx-\frac {1}{7} \left (2048 \left (512+\sqrt {14}\right )\right ) \int \frac {e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}}}{\left (1024+2 \sqrt {14}-4 x\right )^2} \, dx+\int e^{\frac {x \left (131067-1024 x+2 x^2\right )}{131065-1024 x+2 x^2}} \, dx \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx=e^{x+\frac {2 x}{131065-1024 x+2 x^2}}+16 \log (x) \]
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Time = 6.38 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29
method | result | size |
risch | \(16 \ln \left (x \right )+{\mathrm e}^{\frac {x \left (2 x^{2}-1024 x +131067\right )}{2 x^{2}-1024 x +131065}}\) | \(31\) |
parallelrisch | \(16 \ln \left (x \right )+{\mathrm e}^{\frac {2 x^{3}-1024 x^{2}+131067 x}{2 x^{2}-1024 x +131065}}\) | \(34\) |
norman | \(\frac {-1024 x \,{\mathrm e}^{\frac {2 x^{3}-1024 x^{2}+131067 x}{2 x^{2}-1024 x +131065}}+2 x^{2} {\mathrm e}^{\frac {2 x^{3}-1024 x^{2}+131067 x}{2 x^{2}-1024 x +131065}}+131065 \,{\mathrm e}^{\frac {2 x^{3}-1024 x^{2}+131067 x}{2 x^{2}-1024 x +131065}}}{2 x^{2}-1024 x +131065}+16 \ln \left (x \right )\) | \(114\) |
parts | \(\frac {-1024 x \,{\mathrm e}^{\frac {2 x^{3}-1024 x^{2}+131067 x}{2 x^{2}-1024 x +131065}}+2 x^{2} {\mathrm e}^{\frac {2 x^{3}-1024 x^{2}+131067 x}{2 x^{2}-1024 x +131065}}+131065 \,{\mathrm e}^{\frac {2 x^{3}-1024 x^{2}+131067 x}{2 x^{2}-1024 x +131065}}}{2 x^{2}-1024 x +131065}+16 \ln \left (x \right )\) | \(114\) |
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Time = 0.23 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38 \[ \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx=e^{\left (\frac {2 \, x^{3} - 1024 \, x^{2} + 131067 \, x}{2 \, x^{2} - 1024 \, x + 131065}\right )} + 16 \, \log \left (x\right ) \]
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Time = 0.12 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx=e^{\frac {2 x^{3} - 1024 x^{2} + 131067 x}{2 x^{2} - 1024 x + 131065}} + 16 \log {\left (x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (22) = 44\).
Time = 14.69 (sec) , antiderivative size = 116, normalized size of antiderivative = 4.83 \[ \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx=-\frac {8 \, {\left (67119616 \, x - 17179869135\right )}}{7 \, {\left (2 \, x^{2} - 1024 \, x + 131065\right )}} + \frac {16384 \, {\left (131079 \, x - 33552640\right )}}{7 \, {\left (2 \, x^{2} - 1024 \, x + 131065\right )}} - \frac {6291344 \, {\left (512 \, x - 131065\right )}}{7 \, {\left (2 \, x^{2} - 1024 \, x + 131065\right )}} - \frac {1048520 \, {\left (512 \, x - 131079\right )}}{7 \, {\left (2 \, x^{2} - 1024 \, x + 131065\right )}} + \frac {2147368960 \, {\left (x - 256\right )}}{7 \, {\left (2 \, x^{2} - 1024 \, x + 131065\right )}} + e^{\left (x + \frac {2 \, x}{2 \, x^{2} - 1024 \, x + 131065}\right )} + 16 \, \log \left (x\right ) \]
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Time = 0.35 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.38 \[ \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx=e^{\left (\frac {2 \, x^{3} - 1024 \, x^{2} + 131067 \, x}{2 \, x^{2} - 1024 \, x + 131065}\right )} + 16 \, \log \left (x\right ) \]
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Time = 7.75 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.42 \[ \int \frac {274848547600-4294737920 x+25165376 x^2-65536 x^3+64 x^4+e^{\frac {131067 x-1024 x^2+2 x^3}{131065-1024 x+2 x^2}} \left (17178296355 x-268421120 x^2+1572832 x^3-4096 x^4+4 x^5\right )}{17178034225 x-268421120 x^2+1572836 x^3-4096 x^4+4 x^5} \, dx=16\,\ln \left (x\right )+{\mathrm {e}}^{\frac {131067\,x}{2\,x^2-1024\,x+131065}}\,{\mathrm {e}}^{\frac {2\,x^3}{2\,x^2-1024\,x+131065}}\,{\mathrm {e}}^{-\frac {1024\,x^2}{2\,x^2-1024\,x+131065}} \]
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