Integrand size = 510, antiderivative size = 28 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16}{\left (x+\frac {x}{-3+e^{-5+\frac {1}{3} x \log (4)}+x}\right )^4 \log (x)} \]
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\[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {16 \left (2^{2 x/3}+e^5 (-3+x)\right )^3 \left (-3 \left (2^{4 x/3}+2^{2 x/3} e^5 (-5+2 x)+e^{10} \left (6-5 x+x^2\right )\right )-4 \left (3\ 2^{4 x/3}+3 e^{10} \left (6-6 x+x^2\right )-2^{2 x/3} e^5 (15+x (-6+\log (4)))\right ) \log (x)\right )}{3 \left (2^{2 x/3}+e^5 (-2+x)\right )^5 x^5 \log ^2(x)} \, dx \\ & = \frac {16}{3} \int \frac {\left (2^{2 x/3}+e^5 (-3+x)\right )^3 \left (-3 \left (2^{4 x/3}+2^{2 x/3} e^5 (-5+2 x)+e^{10} \left (6-5 x+x^2\right )\right )-4 \left (3\ 2^{4 x/3}+3 e^{10} \left (6-6 x+x^2\right )-2^{2 x/3} e^5 (15+x (-6+\log (4)))\right ) \log (x)\right )}{\left (2^{2 x/3}+e^5 (-2+x)\right )^5 x^5 \log ^2(x)} \, dx \\ & = \frac {16}{3} \int \left (\frac {4 e^{25} (-3-2 \log (4)+x \log (4))}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)}-\frac {3 (1+4 \log (x))}{x^5 \log ^2(x)}+\frac {4 e^5 (3+12 \log (x)+x \log (4) \log (x))}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log ^2(x)}+\frac {2 e^{10} \left (-9-36 \log (x)+6 x \left (1-\frac {2 \log (2)}{3}\right ) \log (x)-2 x^2 \log (4) \log (x)\right )}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log ^2(x)}+\frac {12 e^{15} \left (1+4 \log (x)-3 x \left (1+\frac {2 \log (2)}{3}\right ) \log (x)+x^2 \log (4) \log (x)\right )}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log ^2(x)}+\frac {e^{20} \left (-3-12 \log (x)+36 x \left (1+\frac {5 \log (4)}{9}\right ) \log (x)-4 x^2 \log (64) \log (x)\right )}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log ^2(x)}\right ) \, dx \\ & = -\left (16 \int \frac {1+4 \log (x)}{x^5 \log ^2(x)} \, dx\right )+\frac {1}{3} \left (64 e^5\right ) \int \frac {3+12 \log (x)+x \log (4) \log (x)}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log ^2(x)} \, dx+\frac {1}{3} \left (32 e^{10}\right ) \int \frac {-9-36 \log (x)+6 x \left (1-\frac {2 \log (2)}{3}\right ) \log (x)-2 x^2 \log (4) \log (x)}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log ^2(x)} \, dx+\left (64 e^{15}\right ) \int \frac {1+4 \log (x)-3 x \left (1+\frac {2 \log (2)}{3}\right ) \log (x)+x^2 \log (4) \log (x)}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log ^2(x)} \, dx+\frac {1}{3} \left (16 e^{20}\right ) \int \frac {-3-12 \log (x)+36 x \left (1+\frac {5 \log (4)}{9}\right ) \log (x)-4 x^2 \log (64) \log (x)}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log ^2(x)} \, dx+\frac {1}{3} \left (64 e^{25}\right ) \int \frac {-3-2 \log (4)+x \log (4)}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)} \, dx \\ & = 64 \text {Ei}(-4 \log (x)) (1+4 \log (x))+\frac {16 (1+4 \log (x))}{x^4 \log (x)}+64 \int \left (-\frac {4 \text {Ei}(-4 \log (x))}{x}-\frac {1}{x^5 \log (x)}\right ) \, dx+\frac {1}{3} \left (64 e^5\right ) \int \left (\frac {3}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log ^2(x)}+\frac {12}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log (x)}+\frac {\log (4)}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log (x)}\right ) \, dx+\frac {1}{3} \left (32 e^{10}\right ) \int \left (-\frac {9}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log ^2(x)}-\frac {36}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)}+\frac {2 (3-\log (4))}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)}-\frac {2 \log (4)}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)}\right ) \, dx+\left (64 e^{15}\right ) \int \left (\frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log ^2(x)}+\frac {4}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)}+\frac {\log (4)}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)}-\frac {3+\log (4)}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)}\right ) \, dx+\frac {1}{3} \left (16 e^{20}\right ) \int \left (-\frac {3}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log ^2(x)}-\frac {12}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)}+\frac {4 (9+5 \log (4))}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)}-\frac {4 \log (64)}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)}\right ) \, dx+\frac {1}{3} \left (64 e^{25}\right ) \int \left (\frac {\log (4)}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)}+\frac {-3-\log (16)}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)}\right ) \, dx \\ & = 64 \text {Ei}(-4 \log (x)) (1+4 \log (x))+\frac {16 (1+4 \log (x))}{x^4 \log (x)}-64 \int \frac {1}{x^5 \log (x)} \, dx-256 \int \frac {\text {Ei}(-4 \log (x))}{x} \, dx+\left (64 e^5\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log ^2(x)} \, dx+\left (256 e^5\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log (x)} \, dx-\left (96 e^{10}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log ^2(x)} \, dx-\left (384 e^{10}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\left (64 e^{15}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log ^2(x)} \, dx+\left (256 e^{15}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx-\left (16 e^{20}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log ^2(x)} \, dx-\left (64 e^{20}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx+\frac {1}{3} \left (64 e^{10} (3-\log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\frac {1}{3} \left (64 e^5 \log (4)\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log (x)} \, dx-\frac {1}{3} \left (64 e^{10} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\left (64 e^{15} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx+\frac {1}{3} \left (64 e^{25} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)} \, dx-\left (64 e^{15} (3+\log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx+\frac {1}{3} \left (64 e^{20} (9+5 \log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx-\frac {1}{3} \left (64 e^{25} (3+\log (16))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)} \, dx-\frac {1}{3} \left (64 e^{20} \log (64)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx \\ & = 64 \text {Ei}(-4 \log (x)) (1+4 \log (x))+\frac {16 (1+4 \log (x))}{x^4 \log (x)}-64 \text {Subst}\left (\int \frac {e^{-4 x}}{x} \, dx,x,\log (x)\right )-256 \text {Subst}(\int \text {Ei}(-4 x) \, dx,x,\log (x))+\left (64 e^5\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log ^2(x)} \, dx+\left (256 e^5\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log (x)} \, dx-\left (96 e^{10}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log ^2(x)} \, dx-\left (384 e^{10}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\left (64 e^{15}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log ^2(x)} \, dx+\left (256 e^{15}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx-\left (16 e^{20}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log ^2(x)} \, dx-\left (64 e^{20}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx+\frac {1}{3} \left (64 e^{10} (3-\log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\frac {1}{3} \left (64 e^5 \log (4)\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log (x)} \, dx-\frac {1}{3} \left (64 e^{10} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\left (64 e^{15} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx+\frac {1}{3} \left (64 e^{25} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)} \, dx-\left (64 e^{15} (3+\log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx+\frac {1}{3} \left (64 e^{20} (9+5 \log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx-\frac {1}{3} \left (64 e^{25} (3+\log (16))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)} \, dx-\frac {1}{3} \left (64 e^{20} \log (64)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx \\ & = -\frac {64}{x^4}-64 \text {Ei}(-4 \log (x))-256 \text {Ei}(-4 \log (x)) \log (x)+64 \text {Ei}(-4 \log (x)) (1+4 \log (x))+\frac {16 (1+4 \log (x))}{x^4 \log (x)}+\left (64 e^5\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log ^2(x)} \, dx+\left (256 e^5\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log (x)} \, dx-\left (96 e^{10}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log ^2(x)} \, dx-\left (384 e^{10}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\left (64 e^{15}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log ^2(x)} \, dx+\left (256 e^{15}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx-\left (16 e^{20}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log ^2(x)} \, dx-\left (64 e^{20}\right ) \int \frac {1}{x^5 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx+\frac {1}{3} \left (64 e^{10} (3-\log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\frac {1}{3} \left (64 e^5 \log (4)\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right ) \log (x)} \, dx-\frac {1}{3} \left (64 e^{10} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^2 \log (x)} \, dx+\left (64 e^{15} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx+\frac {1}{3} \left (64 e^{25} \log (4)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)} \, dx-\left (64 e^{15} (3+\log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^3 \log (x)} \, dx+\frac {1}{3} \left (64 e^{20} (9+5 \log (4))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx-\frac {1}{3} \left (64 e^{25} (3+\log (16))\right ) \int \frac {1}{x^4 \left (2^{2 x/3}-2 e^5+e^5 x\right )^5 \log (x)} \, dx-\frac {1}{3} \left (64 e^{20} \log (64)\right ) \int \frac {1}{x^3 \left (2^{2 x/3}-2 e^5+e^5 x\right )^4 \log (x)} \, dx \\ \end{align*}
Time = 0.31 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.54 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \left (2^{2 x/3}+e^5 (-3+x)\right )^4}{\left (2^{2 x/3}+e^5 (-2+x)\right )^4 x^4 \log (x)} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(273\) vs. \(2(25)=50\).
Time = 17.80 (sec) , antiderivative size = 274, normalized size of antiderivative = 9.79
method | result | size |
risch | \(\frac {16 x^{4}+64 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x^{3}+96 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10} x^{2}+64 \,2^{2 x} {\mathrm e}^{-15} x +16 \,2^{\frac {8 x}{3}} {\mathrm e}^{-20}-192 x^{3}-576 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x^{2}-576 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10} x -192 \,2^{2 x} {\mathrm e}^{-15}+864 x^{2}+1728 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x +864 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10}-1728 x -1728 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5}+1296}{x^{4} \left (x^{4}+4 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x^{3}+6 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10} x^{2}+4 \,2^{2 x} {\mathrm e}^{-15} x +2^{\frac {8 x}{3}} {\mathrm e}^{-20}-8 x^{3}-24 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x^{2}-24 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10} x -8 \,2^{2 x} {\mathrm e}^{-15}+24 x^{2}+48 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x +24 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10}-32 x -32 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5}+16\right ) \ln \left (x \right )}\) | \(274\) |
parallelrisch | \(\frac {3888+48 \,{\mathrm e}^{\frac {8 x \ln \left (2\right )}{3}-20}-576 \,{\mathrm e}^{2 x \ln \left (2\right )-15}+2592 \,{\mathrm e}^{\frac {4 x \ln \left (2\right )}{3}-10}+5184 \,{\mathrm e}^{\frac {2 x \ln \left (2\right )}{3}-5} x +288 \,{\mathrm e}^{\frac {4 x \ln \left (2\right )}{3}-10} x^{2}+192 \,{\mathrm e}^{\frac {2 x \ln \left (2\right )}{3}-5} x^{3}-1728 \,{\mathrm e}^{\frac {4 x \ln \left (2\right )}{3}-10} x -1728 \,{\mathrm e}^{\frac {2 x \ln \left (2\right )}{3}-5} x^{2}+192 \,{\mathrm e}^{2 x \ln \left (2\right )-15} x -5184 x -5184 \,{\mathrm e}^{\frac {2 x \ln \left (2\right )}{3}-5}+48 x^{4}-576 x^{3}+2592 x^{2}}{3 x^{4} \ln \left (x \right ) \left (x^{4}+4 \,{\mathrm e}^{\frac {2 x \ln \left (2\right )}{3}-5} x^{3}+6 \,{\mathrm e}^{\frac {4 x \ln \left (2\right )}{3}-10} x^{2}+4 \,{\mathrm e}^{2 x \ln \left (2\right )-15} x +{\mathrm e}^{\frac {8 x \ln \left (2\right )}{3}-20}-8 x^{3}-24 \,{\mathrm e}^{\frac {2 x \ln \left (2\right )}{3}-5} x^{2}-24 \,{\mathrm e}^{\frac {4 x \ln \left (2\right )}{3}-10} x -8 \,{\mathrm e}^{2 x \ln \left (2\right )-15}+24 x^{2}+48 \,{\mathrm e}^{\frac {2 x \ln \left (2\right )}{3}-5} x +24 \,{\mathrm e}^{\frac {4 x \ln \left (2\right )}{3}-10}-32 x -32 \,{\mathrm e}^{\frac {2 x \ln \left (2\right )}{3}-5}+16\right )}\) | \(296\) |
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Leaf count of result is larger than twice the leaf count of optimal. 196 vs. \(2 (25) = 50\).
Time = 0.25 (sec) , antiderivative size = 196, normalized size of antiderivative = 7.00 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} + 4 \, {\left (x - 3\right )} e^{\left (2 \, x \log \left (2\right ) - 15\right )} + 6 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (\frac {4}{3} \, x \log \left (2\right ) - 10\right )} + 4 \, {\left (x^{3} - 9 \, x^{2} + 27 \, x - 27\right )} e^{\left (\frac {2}{3} \, x \log \left (2\right ) - 5\right )} - 108 \, x + e^{\left (\frac {8}{3} \, x \log \left (2\right ) - 20\right )} + 81\right )}}{{\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + x^{4} e^{\left (\frac {8}{3} \, x \log \left (2\right ) - 20\right )} + 16 \, x^{4} + 4 \, {\left (x^{5} - 2 \, x^{4}\right )} e^{\left (2 \, x \log \left (2\right ) - 15\right )} + 6 \, {\left (x^{6} - 4 \, x^{5} + 4 \, x^{4}\right )} e^{\left (\frac {4}{3} \, x \log \left (2\right ) - 10\right )} + 4 \, {\left (x^{7} - 6 \, x^{6} + 12 \, x^{5} - 8 \, x^{4}\right )} e^{\left (\frac {2}{3} \, x \log \left (2\right ) - 5\right )}\right )} \log \left (x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 243 vs. \(2 (24) = 48\).
Time = 0.62 (sec) , antiderivative size = 243, normalized size of antiderivative = 8.68 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {- 64 x^{3} + 480 x^{2} - 1216 x + \left (480 - 192 x\right ) e^{\frac {4 x \log {\left (2 \right )}}{3} - 10} + \left (- 192 x^{2} + 960 x - 1216\right ) e^{\frac {2 x \log {\left (2 \right )}}{3} - 5} - 64 e^{2 x \log {\left (2 \right )} - 15} + 1040}{x^{8} \log {\left (x \right )} - 8 x^{7} \log {\left (x \right )} + 24 x^{6} \log {\left (x \right )} - 32 x^{5} \log {\left (x \right )} + x^{4} e^{\frac {8 x \log {\left (2 \right )}}{3} - 20} \log {\left (x \right )} + 16 x^{4} \log {\left (x \right )} + \left (4 x^{5} \log {\left (x \right )} - 8 x^{4} \log {\left (x \right )}\right ) e^{2 x \log {\left (2 \right )} - 15} + \left (6 x^{6} \log {\left (x \right )} - 24 x^{5} \log {\left (x \right )} + 24 x^{4} \log {\left (x \right )}\right ) e^{\frac {4 x \log {\left (2 \right )}}{3} - 10} + \left (4 x^{7} \log {\left (x \right )} - 24 x^{6} \log {\left (x \right )} + 48 x^{5} \log {\left (x \right )} - 32 x^{4} \log {\left (x \right )}\right ) e^{\frac {2 x \log {\left (2 \right )}}{3} - 5}} + \frac {16}{x^{4} \log {\left (x \right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 248 vs. \(2 (25) = 50\).
Time = 0.85 (sec) , antiderivative size = 248, normalized size of antiderivative = 8.86 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \, {\left (x^{4} e^{20} - 12 \, x^{3} e^{20} + 54 \, x^{2} e^{20} + 4 \, {\left (x e^{5} - 3 \, e^{5}\right )} 2^{2 \, x} + 6 \, {\left (x^{2} e^{10} - 6 \, x e^{10} + 9 \, e^{10}\right )} 2^{\frac {4}{3} \, x} + 4 \, {\left (x^{3} e^{15} - 9 \, x^{2} e^{15} + 27 \, x e^{15} - 27 \, e^{15}\right )} 2^{\frac {2}{3} \, x} - 108 \, x e^{20} + 2^{\frac {8}{3} \, x} + 81 \, e^{20}\right )}}{2^{\frac {8}{3} \, x} x^{4} \log \left (x\right ) + 4 \, {\left (x^{5} e^{5} - 2 \, x^{4} e^{5}\right )} 2^{2 \, x} \log \left (x\right ) + 6 \, {\left (x^{6} e^{10} - 4 \, x^{5} e^{10} + 4 \, x^{4} e^{10}\right )} 2^{\frac {4}{3} \, x} \log \left (x\right ) + 4 \, {\left (x^{7} e^{15} - 6 \, x^{6} e^{15} + 12 \, x^{5} e^{15} - 8 \, x^{4} e^{15}\right )} 2^{\frac {2}{3} \, x} \log \left (x\right ) + {\left (x^{8} e^{20} - 8 \, x^{7} e^{20} + 24 \, x^{6} e^{20} - 32 \, x^{5} e^{20} + 16 \, x^{4} e^{20}\right )} \log \left (x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 314 vs. \(2 (25) = 50\).
Time = 1.84 (sec) , antiderivative size = 314, normalized size of antiderivative = 11.21 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \, {\left (x^{4} e^{20} + 4 \cdot 2^{\frac {2}{3} \, x} x^{3} e^{15} - 12 \, x^{3} e^{20} - 36 \cdot 2^{\frac {2}{3} \, x} x^{2} e^{15} + 6 \cdot 2^{\frac {4}{3} \, x} x^{2} e^{10} + 54 \, x^{2} e^{20} + 108 \cdot 2^{\frac {2}{3} \, x} x e^{15} - 36 \cdot 2^{\frac {4}{3} \, x} x e^{10} + 4 \cdot 2^{2 \, x} x e^{5} - 108 \, x e^{20} - 108 \cdot 2^{\frac {2}{3} \, x} e^{15} + 54 \cdot 2^{\frac {4}{3} \, x} e^{10} - 12 \cdot 2^{2 \, x} e^{5} + 2^{\frac {8}{3} \, x} + 81 \, e^{20}\right )}}{x^{8} e^{20} \log \left (x\right ) + 4 \cdot 2^{\frac {2}{3} \, x} x^{7} e^{15} \log \left (x\right ) - 8 \, x^{7} e^{20} \log \left (x\right ) - 24 \cdot 2^{\frac {2}{3} \, x} x^{6} e^{15} \log \left (x\right ) + 6 \cdot 2^{\frac {4}{3} \, x} x^{6} e^{10} \log \left (x\right ) + 24 \, x^{6} e^{20} \log \left (x\right ) + 48 \cdot 2^{\frac {2}{3} \, x} x^{5} e^{15} \log \left (x\right ) - 24 \cdot 2^{\frac {4}{3} \, x} x^{5} e^{10} \log \left (x\right ) + 4 \cdot 2^{2 \, x} x^{5} e^{5} \log \left (x\right ) - 32 \, x^{5} e^{20} \log \left (x\right ) - 32 \cdot 2^{\frac {2}{3} \, x} x^{4} e^{15} \log \left (x\right ) + 24 \cdot 2^{\frac {4}{3} \, x} x^{4} e^{10} \log \left (x\right ) - 8 \cdot 2^{2 \, x} x^{4} e^{5} \log \left (x\right ) + 2^{\frac {8}{3} \, x} x^{4} \log \left (x\right ) + 16 \, x^{4} e^{20} \log \left (x\right )} \]
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Timed out. \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\int -\frac {14256\,x+48\,{\mathrm {e}}^{\frac {10\,x\,\ln \left (2\right )}{3}-25}+{\mathrm {e}}^{\frac {4\,x\,\ln \left (2\right )}{3}-10}\,\left (480\,x^3-4032\,x^2+11232\,x-10368\right )+\ln \left (x\right )\,\left (62208\,x+192\,{\mathrm {e}}^{\frac {10\,x\,\ln \left (2\right )}{3}-25}+{\mathrm {e}}^{2\,x\,\ln \left (2\right )-15}\,\left (2\,\ln \left (2\right )\,\left (576\,x-192\,x^2\right )-10944\,x+1920\,x^2+14976\right )-{\mathrm {e}}^{\frac {4\,x\,\ln \left (2\right )}{3}-10}\,\left (2\,\ln \left (2\right )\,\left (192\,x^3-1152\,x^2+1728\,x\right )-46656\,x+16704\,x^2-1920\,x^3+41472\right )-46656\,x^2+16704\,x^3-2880\,x^4+192\,x^5-{\mathrm {e}}^{\frac {8\,x\,\ln \left (2\right )}{3}-20}\,\left (128\,x\,\ln \left (2\right )-960\,x+2688\right )+{\mathrm {e}}^{\frac {2\,x\,\ln \left (2\right )}{3}-5}\,\left (2\,\ln \left (2\right )\,\left (-64\,x^4+576\,x^3-1728\,x^2+1728\,x\right )-88128\,x+48384\,x^2-11328\,x^3+960\,x^4+57024\right )-31104\right )+{\mathrm {e}}^{\frac {2\,x\,\ln \left (2\right )}{3}-5}\,\left (240\,x^4-2688\,x^3+11232\,x^2-20736\,x+14256\right )+{\mathrm {e}}^{\frac {8\,x\,\ln \left (2\right )}{3}-20}\,\left (240\,x-672\right )+{\mathrm {e}}^{2\,x\,\ln \left (2\right )-15}\,\left (480\,x^2-2688\,x+3744\right )-10368\,x^2+3744\,x^3-672\,x^4+48\,x^5-7776}{{\ln \left (x\right )}^2\,\left (3\,x^5\,{\mathrm {e}}^{\frac {10\,x\,\ln \left (2\right )}{3}-25}-{\mathrm {e}}^{\frac {8\,x\,\ln \left (2\right )}{3}-20}\,\left (30\,x^5-15\,x^6\right )+{\mathrm {e}}^{2\,x\,\ln \left (2\right )-15}\,\left (30\,x^7-120\,x^6+120\,x^5\right )-{\mathrm {e}}^{\frac {4\,x\,\ln \left (2\right )}{3}-10}\,\left (-30\,x^8+180\,x^7-360\,x^6+240\,x^5\right )-96\,x^5+240\,x^6-240\,x^7+120\,x^8-30\,x^9+3\,x^{10}+{\mathrm {e}}^{\frac {2\,x\,\ln \left (2\right )}{3}-5}\,\left (15\,x^9-120\,x^8+360\,x^7-480\,x^6+240\,x^5\right )\right )} \,d x \]
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