3.9.0 ∫ 24x2−8x3+64e4x log(−3+x)+e4(96+16x−16x2) log2(−3+x)+e8(24−8x) log4(−3+x) ______________________________________________________________________________________________ −192x2−32x3+20x4+4x5+(48x2−4x3−4x4) log(5)+(−3x2+x3) log2(5)+(e4(−96x2+8x3+8x4)+e4(48x+8x2−8x3) log(5)+e4(−6x+2x2) log2(5)) log2(−3+x)+(e8(−12x2+4x3)+e8(12x−4x2) log(5)+e8(−3+x) log2(5)) log4(−3+x) dx [863]

Integrand size = 227, antiderivative size = 29 \[ \int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx=\frac {4}{2 x-\log (5)+\frac {8 x}{x+e^4 \log ^2(-3+x)}} \]

Rubi [F]

\[ \int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx=\int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx \]

Rubi steps \begin{align*} \text {integral}& = \int \frac {8 \left ((-3+x) x^2-8 e^4 x \log (-3+x)+2 e^4 \left (-6-x+x^2\right ) \log ^2(-3+x)+e^8 (-3+x) \log ^4(-3+x)\right )}{(3-x) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx \\ & = 8 \int \frac {(-3+x) x^2-8 e^4 x \log (-3+x)+2 e^4 \left (-6-x+x^2\right ) \log ^2(-3+x)+e^8 (-3+x) \log ^4(-3+x)}{(3-x) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx \\ & = 8 \int \left (-\frac {1}{(2 x-\log (5))^2}+\frac {4 x \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(3-x) (2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2}+\frac {8 x+\log (625)}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )}\right ) \, dx \\ & = \frac {4}{2 x-\log (5)}+8 \int \frac {8 x+\log (625)}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )} \, dx+32 \int \frac {x \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(3-x) (2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2} \, dx \\ & = \frac {4}{2 x-\log (5)}+8 \int \frac {8 x+\log (625)}{(2 x-\log (5))^2 \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )} \, dx+32 \int \frac {x \left (-\left ((-3+x) \left (4 x^2-4 x \log (5)+(-8+\log (5)) \log (5)\right )\right )-2 e^4 (-2 x+\log (5))^2 \log (-3+x)\right )}{(3-x) (2 x-\log (5))^2 \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx \\ & = \frac {4}{2 x-\log (5)}+8 \int \left (\frac {4}{(2 x-\log (5)) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )}+\frac {2 \log (625)}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )}\right ) \, dx+32 \int \left (\frac {3 \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(3-x) (6-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2}+\frac {6 \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(6-\log (5))^2 (2 x-\log (5)) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2}+\frac {\log (5) \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(6-\log (5)) (2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2}\right ) \, dx \\ & = \frac {4}{2 x-\log (5)}+32 \int \frac {1}{(2 x-\log (5)) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )} \, dx+\frac {96 \int \frac {-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)}{(3-x) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2} \, dx}{(6-\log (5))^2}+\frac {192 \int \frac {-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)}{(2 x-\log (5)) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2} \, dx}{(6-\log (5))^2}+\frac {(32 \log (5)) \int \frac {-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2} \, dx}{6-\log (5)}+(16 \log (625)) \int \frac {1}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )} \, dx \\ & = \frac {4}{2 x-\log (5)}+32 \int \frac {1}{(2 x-\log (5)) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )} \, dx+\frac {96 \int \frac {-\left ((-3+x) \left (4 x^2-4 x \log (5)+(-8+\log (5)) \log (5)\right )\right )-2 e^4 (-2 x+\log (5))^2 \log (-3+x)}{(3-x) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx}{(6-\log (5))^2}+\frac {192 \int \frac {-\left ((-3+x) \left (4 x^2-4 x \log (5)+(-8+\log (5)) \log (5)\right )\right )-2 e^4 (-2 x+\log (5))^2 \log (-3+x)}{(2 x-\log (5)) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx}{(6-\log (5))^2}+\frac {(32 \log (5)) \int \frac {-\left ((-3+x) \left (4 x^2-4 x \log (5)+(-8+\log (5)) \log (5)\right )\right )-2 e^4 (-2 x+\log (5))^2 \log (-3+x)}{(2 x-\log (5))^2 \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx}{6-\log (5)}+(16 \log (625)) \int \frac {1}{(2 x-\log (5))^2 \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (veriﬁed)

Time = 0.12 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.66 \[ \int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx=\frac {8 \left (x+e^4 \log ^2(-3+x)\right )}{2 x (8+2 x-\log (5))+2 e^4 (2 x-\log (5)) \log ^2(-3+x)} \]

Maple [A] (veriﬁed)

Time = 1.67 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.86


method	result	size

parallelrisch	\(\frac {-8 \ln \left (-3+x \right )^{2} {\mathrm e}^{4}-8 x}{2 \ln \left (-3+x \right )^{2} \ln \left (5\right ) {\mathrm e}^{4}-4 \,{\mathrm e}^{4} \ln \left (-3+x \right )^{2} x +2 x \ln \left (5\right )-4 x^{2}-16 x}\)	\(54\)
risch	\(-\frac {4}{\ln \left (5\right )-2 x}-\frac {32 x}{\left (\ln \left (5\right )-2 x \right ) \left (\ln \left (-3+x \right )^{2} \ln \left (5\right ) {\mathrm e}^{4}-2 \,{\mathrm e}^{4} \ln \left (-3+x \right )^{2} x +x \ln \left (5\right )-2 x^{2}-8 x \right )}\)	\(60\)
derivativedivides	\(-\frac {8 \left (\frac {x}{2}+\frac {\ln \left (-3+x \right )^{2} {\mathrm e}^{4}}{2}\right )}{\ln \left (-3+x \right )^{2} \ln \left (5\right ) {\mathrm e}^{4}-2 \,{\mathrm e}^{4} \ln \left (-3+x \right )^{2} \left (-3+x \right )-6 \ln \left (-3+x \right )^{2} {\mathrm e}^{4}+\left (-3+x \right ) \ln \left (5\right )-2 \left (-3+x \right )^{2}+3 \ln \left (5\right )+18-20 x}\)	\(75\)
default	\(-\frac {8 \left (\frac {x}{2}+\frac {\ln \left (-3+x \right )^{2} {\mathrm e}^{4}}{2}\right )}{\ln \left (-3+x \right )^{2} \ln \left (5\right ) {\mathrm e}^{4}-2 \,{\mathrm e}^{4} \ln \left (-3+x \right )^{2} \left (-3+x \right )-6 \ln \left (-3+x \right )^{2} {\mathrm e}^{4}+\left (-3+x \right ) \ln \left (5\right )-2 \left (-3+x \right )^{2}+3 \ln \left (5\right )+18-20 x}\)	\(75\)

Fricas [A] (veriﬁcation not implemented)

Time = 0.26 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.66 \[ \int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx=\frac {4 \, {\left (e^{4} \log \left (x - 3\right )^{2} + x\right )}}{{\left (2 \, x e^{4} - e^{4} \log \left (5\right )\right )} \log \left (x - 3\right )^{2} + 2 \, x^{2} - x \log \left (5\right ) + 8 \, x} \]

Sympy [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (22) = 44\).

Time = 0.29 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.69 \[ \int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx=- \frac {32 x}{4 x^{3} - 4 x^{2} \log {\left (5 \right )} + 16 x^{2} - 8 x \log {\left (5 \right )} + x \log {\left (5 \right )}^{2} + \left (4 x^{2} e^{4} - 4 x e^{4} \log {\left (5 \right )} + e^{4} \log {\left (5 \right )}^{2}\right ) \log {\left (x - 3 \right )}^{2}} + \frac {8}{4 x - 2 \log {\left (5 \right )}} \]

Maxima [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (28) = 56\).

Time = 0.43 (sec) , antiderivative size = 89, normalized size of antiderivative = 3.07 \[ \int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx=\frac {4 \, {\left ({\left (2 \, x e^{4} - e^{4} \log \left (5\right )\right )} \log \left (x - 3\right )^{2} + 2 \, x^{2} - x \log \left (5\right )\right )}}{4 \, x^{3} - 4 \, x^{2} {\left (\log \left (5\right ) - 4\right )} + {\left (4 \, x^{2} e^{4} - 4 \, x e^{4} \log \left (5\right ) + e^{4} \log \left (5\right )^{2}\right )} \log \left (x - 3\right )^{2} + {\left (\log \left (5\right )^{2} - 8 \, \log \left (5\right )\right )} x} \]

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (28) = 56\).

Time = 10.05 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.76 \[ \int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx=\frac {4 \, {\left (2 \, x e^{4} \log \left (x - 3\right )^{2} - e^{4} \log \left (5\right ) \log \left (x - 3\right )^{2} + 2 \, x^{2} - x \log \left (5\right ) - 8 \, x\right )}}{4 \, x^{2} e^{4} \log \left (x - 3\right )^{2} - 4 \, x e^{4} \log \left (5\right ) \log \left (x - 3\right )^{2} + e^{4} \log \left (5\right )^{2} \log \left (x - 3\right )^{2} + 4 \, x^{3} - 4 \, x^{2} \log \left (5\right ) + x \log \left (5\right )^{2} + 16 \, x^{2} - 8 \, x \log \left (5\right )} \]

Mupad [F(-1)]

Timed out. \[ \int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx=\int -\frac {24\,x^2-8\,x^3+64\,x\,\ln \left (x-3\right )\,{\mathrm {e}}^4-{\ln \left (x-3\right )}^4\,{\mathrm {e}}^8\,\left (8\,x-24\right )+{\ln \left (x-3\right )}^2\,{\mathrm {e}}^4\,\left (-16\,x^2+16\,x+96\right )}{\ln \left (5\right )\,\left (4\,x^4+4\,x^3-48\,x^2\right )+192\,x^2+32\,x^3-20\,x^4-4\,x^5+{\ln \left (5\right )}^2\,\left (3\,x^2-x^3\right )-{\ln \left (x-3\right )}^4\,\left ({\mathrm {e}}^8\,{\ln \left (5\right )}^2\,\left (x-3\right )-{\mathrm {e}}^8\,\left (12\,x^2-4\,x^3\right )+{\mathrm {e}}^8\,\ln \left (5\right )\,\left (12\,x-4\,x^2\right )\right )-{\ln \left (x-3\right )}^2\,\left ({\mathrm {e}}^4\,\left (8\,x^4+8\,x^3-96\,x^2\right )+{\mathrm {e}}^4\,\ln \left (5\right )\,\left (-8\,x^3+8\,x^2+48\,x\right )-{\mathrm {e}}^4\,{\ln \left (5\right )}^2\,\left (6\,x-2\,x^2\right )\right )} \,d x \]

Optimal result