\(\int \frac {(-323 x+160 x^2-16 x^3)^{2-5^{\frac {1}{x}}} (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} (-323 x+320 x^2-48 x^3)+5^{\frac {1}{x}} (323-160 x+16 x^2) \log (5) \log (-323 x+160 x^2-16 x^3))}{323 x^3-160 x^4+16 x^5} \, dx\) [3871]

Optimal result

Integrand size = 110, antiderivative size = 31 \[ \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx=\frac {\left (\left (-3+16 \left (5-(5-x)^2\right )\right ) x\right )^{2-5^{\frac {1}{x}}}}{x} \]

[Out]

exp(ln(x*(77-16*(5-x)^2))*(-exp(ln(5)/x)+2))/x

Rubi [F]

\[ \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx=\int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx \]

[In]

Int[((-323*x + 160*x^2 - 16*x^3)^(2 - 5^x^(-1))*(323*x - 480*x^2 + 80*x^3 + 5^x^(-1)*(-323*x + 320*x^2 - 48*x^
3) + 5^x^(-1)*(323 - 160*x + 16*x^2)*Log[5]*Log[-323*x + 160*x^2 - 16*x^3]))/(323*x^3 - 160*x^4 + 16*x^5),x]

[Out]

-20672*Log[5]*Log[-(x*(323 - 160*x + 16*x^2))]*Defer[Int][5^(1 + x^(-1))/(x*(-323 + 160*x - 16*x^2))^5^x^(-1),
x] - 104329*Defer[Int][5^x^(-1)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x] + 104329*Log[5]*Log[-(x*(323 - 160*x
+ 16*x^2))]*Defer[Int][5^x^(-1)/(x*(x*(-323 + 160*x - 16*x^2))^5^x^(-1)), x] + 31008*Defer[Int][(5^(1 + x^(-1
))*x)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x] + 35936*Log[5]*Log[-(x*(323 - 160*x + 16*x^2))]*Defer[Int][(5^x
^(-1)*x)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x] - 1024*Log[5]*Log[-(x*(323 - 160*x + 16*x^2))]*Defer[Int][(5
^(1 + x^(-1))*x^2)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x] - 71872*Defer[Int][(5^x^(-1)*x^2)/(x*(-323 + 160*x
- 16*x^2))^5^x^(-1), x] + 512*Defer[Int][(5^(2 + x^(-1))*x^3)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x] + 256*
Log[5]*Log[-(x*(323 - 160*x + 16*x^2))]*Defer[Int][(5^x^(-1)*x^3)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x] - 7
68*Defer[Int][(5^x^(-1)*x^4)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x] + Defer[Int][(x*(-323 + 160*x - 16*x^2))
^(2 - 5^x^(-1))/x^2, x] - (320*Defer[Int][(x*(-323 + 160*x - 16*x^2))^(2 - 5^x^(-1))/x, x])/323 + (256*(20 - S
qrt[77])*Defer[Int][(x*(-323 + 160*x - 16*x^2))^(2 - 5^x^(-1))/(-160 - 8*Sqrt[77] + 32*x), x])/323 + (256*(20
+ Sqrt[77])*Defer[Int][(x*(-323 + 160*x - 16*x^2))^(2 - 5^x^(-1))/(-160 + 8*Sqrt[77] + 32*x), x])/323 + (13230
080*Log[5]*Defer[Int][Defer[Int][5^(1 + x^(-1))/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(160 + 8*Sqrt[77] - 3
2*x), x])/Sqrt[77] + 20672*Log[5]*Defer[Int][Defer[Int][5^(1 + x^(-1))/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x
]/x, x] + (661504*(77 + 20*Sqrt[77])*Log[5]*Defer[Int][Defer[Int][5^(1 + x^(-1))/(x*(-323 + 160*x - 16*x^2))^5
^x^(-1), x]/(-160 - 8*Sqrt[77] + 32*x), x])/77 + (13230080*Log[5]*Defer[Int][Defer[Int][5^(1 + x^(-1))/(x*(-32
3 + 160*x - 16*x^2))^5^x^(-1), x]/(-160 + 8*Sqrt[77] + 32*x), x])/Sqrt[77] + (661504*(77 - 20*Sqrt[77])*Log[5]
*Defer[Int][Defer[Int][5^(1 + x^(-1))/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(-160 + 8*Sqrt[77] + 32*x), x])
/77 - (66770560*Log[5]*Defer[Int][Defer[Int][5^x^(-1)/(x*(x*(-323 + 160*x - 16*x^2))^5^x^(-1)), x]/(160 + 8*Sq
rt[77] - 32*x), x])/Sqrt[77] - 104329*Log[5]*Defer[Int][Defer[Int][5^x^(-1)/(x*(x*(-323 + 160*x - 16*x^2))^5^x
^(-1)), x]/x, x] - (3338528*(77 + 20*Sqrt[77])*Log[5]*Defer[Int][Defer[Int][5^x^(-1)/(x*(x*(-323 + 160*x - 16*
x^2))^5^x^(-1)), x]/(-160 - 8*Sqrt[77] + 32*x), x])/77 - (66770560*Log[5]*Defer[Int][Defer[Int][5^x^(-1)/(x*(x
*(-323 + 160*x - 16*x^2))^5^x^(-1)), x]/(-160 + 8*Sqrt[77] + 32*x), x])/Sqrt[77] - (3338528*(77 - 20*Sqrt[77])
*Log[5]*Defer[Int][Defer[Int][5^x^(-1)/(x*(x*(-323 + 160*x - 16*x^2))^5^x^(-1)), x]/(-160 + 8*Sqrt[77] + 32*x)
, x])/77 - (22999040*Log[5]*Defer[Int][Defer[Int][(5^x^(-1)*x)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(160 +
8*Sqrt[77] - 32*x), x])/Sqrt[77] - 35936*Log[5]*Defer[Int][Defer[Int][(5^x^(-1)*x)/(x*(-323 + 160*x - 16*x^2)
)^5^x^(-1), x]/x, x] - (1149952*(77 + 20*Sqrt[77])*Log[5]*Defer[Int][Defer[Int][(5^x^(-1)*x)/(x*(-323 + 160*x
- 16*x^2))^5^x^(-1), x]/(-160 - 8*Sqrt[77] + 32*x), x])/77 - (22999040*Log[5]*Defer[Int][Defer[Int][(5^x^(-1)*
x)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(-160 + 8*Sqrt[77] + 32*x), x])/Sqrt[77] - (1149952*(77 - 20*Sqrt[
77])*Log[5]*Defer[Int][Defer[Int][(5^x^(-1)*x)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(-160 + 8*Sqrt[77] + 3
2*x), x])/77 + (655360*Log[5]*Defer[Int][Defer[Int][(5^(1 + x^(-1))*x^2)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1),
x]/(160 + 8*Sqrt[77] - 32*x), x])/Sqrt[77] + 1024*Log[5]*Defer[Int][Defer[Int][(5^(1 + x^(-1))*x^2)/(x*(-323
+ 160*x - 16*x^2))^5^x^(-1), x]/x, x] + (32768*(77 + 20*Sqrt[77])*Log[5]*Defer[Int][Defer[Int][(5^(1 + x^(-1))
*x^2)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(-160 - 8*Sqrt[77] + 32*x), x])/77 + (655360*Log[5]*Defer[Int][
Defer[Int][(5^(1 + x^(-1))*x^2)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(-160 + 8*Sqrt[77] + 32*x), x])/Sqrt[
77] + (32768*(77 - 20*Sqrt[77])*Log[5]*Defer[Int][Defer[Int][(5^(1 + x^(-1))*x^2)/(x*(-323 + 160*x - 16*x^2))^
5^x^(-1), x]/(-160 + 8*Sqrt[77] + 32*x), x])/77 - (163840*Log[5]*Defer[Int][Defer[Int][(5^x^(-1)*x^3)/(x*(-323
+ 160*x - 16*x^2))^5^x^(-1), x]/(160 + 8*Sqrt[77] - 32*x), x])/Sqrt[77] - 256*Log[5]*Defer[Int][Defer[Int][(5
^x^(-1)*x^3)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/x, x] - (8192*(77 + 20*Sqrt[77])*Log[5]*Defer[Int][Defer
[Int][(5^x^(-1)*x^3)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(-160 - 8*Sqrt[77] + 32*x), x])/77 - (163840*Log
[5]*Defer[Int][Defer[Int][(5^x^(-1)*x^3)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1), x]/(-160 + 8*Sqrt[77] + 32*x),
x])/Sqrt[77] - (8192*(77 - 20*Sqrt[77])*Log[5]*Defer[Int][Defer[Int][(5^x^(-1)*x^3)/(x*(-323 + 160*x - 16*x^2)
)^5^x^(-1), x]/(-160 + 8*Sqrt[77] + 32*x), x])/77

Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{x^3 \left (323-160 x+16 x^2\right )} \, dx \\ & = \int \left (\frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}} \left (323-480 x+80 x^2\right )}{x^2 \left (323-160 x+16 x^2\right )}-\frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}} \left (323 x-320 x^2+48 x^3-323 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )+160 x \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )-16 x^2 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right )}{x^3 \left (323-160 x+16 x^2\right )}\right ) \, dx \\ & = \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}} \left (323-480 x+80 x^2\right )}{x^2 \left (323-160 x+16 x^2\right )} \, dx-\int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}} \left (323 x-320 x^2+48 x^3-323 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )+160 x \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )-16 x^2 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right )}{x^3 \left (323-160 x+16 x^2\right )} \, dx \\ & = \int \left (\frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x^2}-\frac {320 \left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{323 x}+\frac {64 (-477+80 x) \left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{323 \left (323-160 x+16 x^2\right )}\right ) \, dx-\int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \left (323-160 x+16 x^2\right ) \left (x \left (323-320 x+48 x^2\right )+\left (-323+160 x-16 x^2\right ) \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right )}{x} \, dx \\ & = \frac {64}{323} \int \frac {(-477+80 x) \left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{323-160 x+16 x^2} \, dx-\frac {320}{323} \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x} \, dx+\int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x^2} \, dx-\int \left (5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \left (323-160 x+16 x^2\right ) \left (323-320 x+48 x^2\right )-\frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \left (323-160 x+16 x^2\right )^2 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )}{x}\right ) \, dx \\ & = \frac {64}{323} \int \left (\frac {\left (80-4 \sqrt {77}\right ) \left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160-8 \sqrt {77}+32 x}+\frac {\left (80+4 \sqrt {77}\right ) \left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160+8 \sqrt {77}+32 x}\right ) \, dx-\frac {320}{323} \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x} \, dx+\log (5) \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \left (323-160 x+16 x^2\right )^2 \log \left (x \left (-323+160 x-16 x^2\right )\right )}{x} \, dx+\int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x^2} \, dx-\int 5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \left (323-160 x+16 x^2\right ) \left (323-320 x+48 x^2\right ) \, dx \\ & = -\left (\frac {320}{323} \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x} \, dx\right )+\frac {1}{323} \left (256 \left (20-\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160-8 \sqrt {77}+32 x} \, dx+\frac {1}{323} \left (256 \left (20+\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160+8 \sqrt {77}+32 x} \, dx-\log (5) \int \frac {\left (323-320 x+48 x^2\right ) \left (-20672 \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+104329 \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx+32 \left (1123 \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-32 \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+8 \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx\right )\right )}{x \left (323-160 x+16 x^2\right )} \, dx+\left (256 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (1024 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (20672 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (35936 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (104329 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx+\int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x^2} \, dx-\int \left (104329\ 5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}-31008\ 5^{1+\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}+71872\ 5^{\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}-512\ 5^{2+\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}+768\ 5^{\frac {1}{x}} x^4 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}\right ) \, dx \\ & = -\left (\frac {320}{323} \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x} \, dx\right )+512 \int 5^{2+\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-768 \int 5^{\frac {1}{x}} x^4 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+31008 \int 5^{1+\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-71872 \int 5^{\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-104329 \int 5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\frac {1}{323} \left (256 \left (20-\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160-8 \sqrt {77}+32 x} \, dx+\frac {1}{323} \left (256 \left (20+\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160+8 \sqrt {77}+32 x} \, dx-\log (5) \int \left (-\frac {\left (323-320 x+48 x^2\right ) \left (20672 \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-104329 \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx-35936 \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+1024 \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx\right )}{x \left (323-160 x+16 x^2\right )}+\frac {256 \left (323-320 x+48 x^2\right ) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx}{x \left (323-160 x+16 x^2\right )}\right ) \, dx+\left (256 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (1024 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (20672 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (35936 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (104329 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx+\int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x^2} \, dx \\ & = -\left (\frac {320}{323} \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x} \, dx\right )+512 \int 5^{2+\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-768 \int 5^{\frac {1}{x}} x^4 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+31008 \int 5^{1+\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-71872 \int 5^{\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-104329 \int 5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\frac {1}{323} \left (256 \left (20-\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160-8 \sqrt {77}+32 x} \, dx+\frac {1}{323} \left (256 \left (20+\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160+8 \sqrt {77}+32 x} \, dx+\log (5) \int \frac {\left (323-320 x+48 x^2\right ) \left (20672 \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-104329 \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx-35936 \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+1024 \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx\right )}{x \left (323-160 x+16 x^2\right )} \, dx-(256 \log (5)) \int \frac {\left (323-320 x+48 x^2\right ) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx}{x \left (323-160 x+16 x^2\right )} \, dx+\left (256 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (1024 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (20672 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (35936 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (104329 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx+\int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x^2} \, dx \\ & = -\left (\frac {320}{323} \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x} \, dx\right )+512 \int 5^{2+\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-768 \int 5^{\frac {1}{x}} x^4 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+31008 \int 5^{1+\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-71872 \int 5^{\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-104329 \int 5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\frac {1}{323} \left (256 \left (20-\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160-8 \sqrt {77}+32 x} \, dx+\frac {1}{323} \left (256 \left (20+\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160+8 \sqrt {77}+32 x} \, dx+\log (5) \int \left (\frac {\left (323-320 x+48 x^2\right ) \left (20672 \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-104329 \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx-35936 \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx\right )}{x \left (323-160 x+16 x^2\right )}+\frac {1024 \left (323-320 x+48 x^2\right ) \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx}{x \left (323-160 x+16 x^2\right )}\right ) \, dx-(256 \log (5)) \int \left (\frac {\int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx}{x}+\frac {32 (-5+x) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx}{323-160 x+16 x^2}\right ) \, dx+\left (256 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (1024 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (20672 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (35936 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (104329 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx+\int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x^2} \, dx \\ & = -\left (\frac {320}{323} \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x} \, dx\right )+512 \int 5^{2+\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-768 \int 5^{\frac {1}{x}} x^4 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+31008 \int 5^{1+\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-71872 \int 5^{\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-104329 \int 5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\frac {1}{323} \left (256 \left (20-\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160-8 \sqrt {77}+32 x} \, dx+\frac {1}{323} \left (256 \left (20+\sqrt {77}\right )\right ) \int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{-160+8 \sqrt {77}+32 x} \, dx+\log (5) \int \frac {\left (323-320 x+48 x^2\right ) \left (20672 \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-104329 \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx-35936 \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx\right )}{x \left (323-160 x+16 x^2\right )} \, dx-(256 \log (5)) \int \frac {\int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx}{x} \, dx+(1024 \log (5)) \int \frac {\left (323-320 x+48 x^2\right ) \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx}{x \left (323-160 x+16 x^2\right )} \, dx-(8192 \log (5)) \int \frac {(-5+x) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx}{323-160 x+16 x^2} \, dx+\left (256 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x^3 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (1024 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} x^2 \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx-\left (20672 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{1+\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (35936 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int 5^{\frac {1}{x}} x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \, dx+\left (104329 \log (5) \log \left (x \left (-323+160 x-16 x^2\right )\right )\right ) \int \frac {5^{\frac {1}{x}} \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}}}{x} \, dx+\int \frac {\left (x \left (-323+160 x-16 x^2\right )\right )^{2-5^{\frac {1}{x}}}}{x^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.14 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.10 \[ \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx=x \left (x \left (-323+160 x-16 x^2\right )\right )^{-5^{\frac {1}{x}}} \left (323-160 x+16 x^2\right )^2 \]

[In]

Integrate[((-323*x + 160*x^2 - 16*x^3)^(2 - 5^x^(-1))*(323*x - 480*x^2 + 80*x^3 + 5^x^(-1)*(-323*x + 320*x^2 -
48*x^3) + 5^x^(-1)*(323 - 160*x + 16*x^2)*Log[5]*Log[-323*x + 160*x^2 - 16*x^3]))/(323*x^3 - 160*x^4 + 16*x^5
),x]

[Out]

(x*(323 - 160*x + 16*x^2)^2)/(x*(-323 + 160*x - 16*x^2))^5^x^(-1)

Maple [A] (verified)

Time = 78.40 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06

method	result	size
parallelrisch	\(\frac {{\mathrm e}^{\left (-{\mathrm e}^{\frac {\ln \left (5\right )}{x}}+2\right ) \ln \left (-16 x^{3}+160 x^{2}-323 x \right )}}{x}\)	\(33\)
risch	\(\frac {{\mathrm e}^{-\frac {\left (5^{\frac {1}{x}}-2\right ) \left (i \pi {\operatorname {csgn}\left (i x \left (x^{2}-10 x +\frac {323}{16}\right )\right )}^{3}+i \pi {\operatorname {csgn}\left (i x \left (x^{2}-10 x +\frac {323}{16}\right )\right )}^{2} \operatorname {csgn}\left (i x \right )+i \pi {\operatorname {csgn}\left (i x \left (x^{2}-10 x +\frac {323}{16}\right )\right )}^{2} \operatorname {csgn}\left (i \left (x^{2}-10 x +\frac {323}{16}\right )\right )-i \pi \,\operatorname {csgn}\left (i x \left (x^{2}-10 x +\frac {323}{16}\right )\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i \left (x^{2}-10 x +\frac {323}{16}\right )\right )-2 i \pi {\operatorname {csgn}\left (i x \left (x^{2}-10 x +\frac {323}{16}\right )\right )}^{2}+2 i \pi +2 \ln \left (x \right )+2 \ln \left (x^{2}-10 x +\frac {323}{16}\right )\right )}{2}}}{x}\)	\(162\)

[In]

int(((16*x^2-160*x+323)*ln(5)*exp(ln(5)/x)*ln(-16*x^3+160*x^2-323*x)+(-48*x^3+320*x^2-323*x)*exp(ln(5)/x)+80*x
^3-480*x^2+323*x)*exp((-exp(ln(5)/x)+2)*ln(-16*x^3+160*x^2-323*x))/(16*x^5-160*x^4+323*x^3),x,method=_RETURNVE
RBOSE)

[Out]

exp((-exp(ln(5)/x)+2)*ln(-16*x^3+160*x^2-323*x))/x

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.90 \[ \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx=\frac {{\left (-16 \, x^{3} + 160 \, x^{2} - 323 \, x\right )}^{-5^{\left (\frac {1}{x}\right )} + 2}}{x} \]

[In]

integrate(((16*x^2-160*x+323)*log(5)*exp(log(5)/x)*log(-16*x^3+160*x^2-323*x)+(-48*x^3+320*x^2-323*x)*exp(log(
5)/x)+80*x^3-480*x^2+323*x)*exp((-exp(log(5)/x)+2)*log(-16*x^3+160*x^2-323*x))/(16*x^5-160*x^4+323*x^3),x, alg
orithm="fricas")

[Out]

(-16*x^3 + 160*x^2 - 323*x)^(-5^(1/x) + 2)/x

Sympy [A] (verification not implemented)

Time = 0.73 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.84 \[ \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx=\frac {e^{\left (2 - e^{\frac {\log {\left (5 \right )}}{x}}\right ) \log {\left (- 16 x^{3} + 160 x^{2} - 323 x \right )}}}{x} \]

[In]

integrate(((16*x**2-160*x+323)*ln(5)*exp(ln(5)/x)*ln(-16*x**3+160*x**2-323*x)+(-48*x**3+320*x**2-323*x)*exp(ln
(5)/x)+80*x**3-480*x**2+323*x)*exp((-exp(ln(5)/x)+2)*ln(-16*x**3+160*x**2-323*x))/(16*x**5-160*x**4+323*x**3),
x)

[Out]

exp((2 - exp(log(5)/x))*log(-16*x**3 + 160*x**2 - 323*x))/x

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (26) = 52\).

Time = 0.31 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.74 \[ \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx={\left (256 \, x^{5} - 5120 \, x^{4} + 35936 \, x^{3} - 103360 \, x^{2} + 104329 \, x\right )} e^{\left (-5^{\left (\frac {1}{x}\right )} \log \left (-16 \, x^{2} + 160 \, x - 323\right ) - 5^{\left (\frac {1}{x}\right )} \log \left (x\right )\right )} \]

[In]

integrate(((16*x^2-160*x+323)*log(5)*exp(log(5)/x)*log(-16*x^3+160*x^2-323*x)+(-48*x^3+320*x^2-323*x)*exp(log(
5)/x)+80*x^3-480*x^2+323*x)*exp((-exp(log(5)/x)+2)*log(-16*x^3+160*x^2-323*x))/(16*x^5-160*x^4+323*x^3),x, alg
orithm="maxima")

[Out]

(256*x^5 - 5120*x^4 + 35936*x^3 - 103360*x^2 + 104329*x)*e^(-5^(1/x)*log(-16*x^2 + 160*x - 323) - 5^(1/x)*log(
x))

Giac [F]

\[ \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx=\int { \frac {{\left ({\left (16 \, x^{2} - 160 \, x + 323\right )} 5^{\left (\frac {1}{x}\right )} \log \left (5\right ) \log \left (-16 \, x^{3} + 160 \, x^{2} - 323 \, x\right ) + 80 \, x^{3} - {\left (48 \, x^{3} - 320 \, x^{2} + 323 \, x\right )} 5^{\left (\frac {1}{x}\right )} - 480 \, x^{2} + 323 \, x\right )} {\left (-16 \, x^{3} + 160 \, x^{2} - 323 \, x\right )}^{-5^{\left (\frac {1}{x}\right )} + 2}}{16 \, x^{5} - 160 \, x^{4} + 323 \, x^{3}} \,d x } \]

[In]

integrate(((16*x^2-160*x+323)*log(5)*exp(log(5)/x)*log(-16*x^3+160*x^2-323*x)+(-48*x^3+320*x^2-323*x)*exp(log(
5)/x)+80*x^3-480*x^2+323*x)*exp((-exp(log(5)/x)+2)*log(-16*x^3+160*x^2-323*x))/(16*x^5-160*x^4+323*x^3),x, alg
orithm="giac")

[Out]

integrate(((16*x^2 - 160*x + 323)*5^(1/x)*log(5)*log(-16*x^3 + 160*x^2 - 323*x) + 80*x^3 - (48*x^3 - 320*x^2 +
323*x)*5^(1/x) - 480*x^2 + 323*x)*(-16*x^3 + 160*x^2 - 323*x)^(-5^(1/x) + 2)/(16*x^5 - 160*x^4 + 323*x^3), x)

Mupad [B] (verification not implemented)

Time = 9.78 (sec) , antiderivative size = 134, normalized size of antiderivative = 4.32 \[ \int \frac {\left (-323 x+160 x^2-16 x^3\right )^{2-5^{\frac {1}{x}}} \left (323 x-480 x^2+80 x^3+5^{\frac {1}{x}} \left (-323 x+320 x^2-48 x^3\right )+5^{\frac {1}{x}} \left (323-160 x+16 x^2\right ) \log (5) \log \left (-323 x+160 x^2-16 x^3\right )\right )}{323 x^3-160 x^4+16 x^5} \, dx=\frac {104329\,x}{{\left (-16\,x^3+160\,x^2-323\,x\right )}^{5^{1/x}}}-\frac {103360\,x^2}{{\left (-16\,x^3+160\,x^2-323\,x\right )}^{5^{1/x}}}+\frac {35936\,x^3}{{\left (-16\,x^3+160\,x^2-323\,x\right )}^{5^{1/x}}}-\frac {5120\,x^4}{{\left (-16\,x^3+160\,x^2-323\,x\right )}^{5^{1/x}}}+\frac {256\,x^5}{{\left (-16\,x^3+160\,x^2-323\,x\right )}^{5^{1/x}}} \]

[In]

int((exp(-log(160*x^2 - 323*x - 16*x^3)*(exp(log(5)/x) - 2))*(323*x - exp(log(5)/x)*(323*x - 320*x^2 + 48*x^3)
- 480*x^2 + 80*x^3 + log(160*x^2 - 323*x - 16*x^3)*exp(log(5)/x)*log(5)*(16*x^2 - 160*x + 323)))/(323*x^3 - 1
60*x^4 + 16*x^5),x)

[Out]

(104329*x)/(160*x^2 - 323*x - 16*x^3)^(5^(1/x)) - (103360*x^2)/(160*x^2 - 323*x - 16*x^3)^(5^(1/x)) + (35936*x
^3)/(160*x^2 - 323*x - 16*x^3)^(5^(1/x)) - (5120*x^4)/(160*x^2 - 323*x - 16*x^3)^(5^(1/x)) + (256*x^5)/(160*x^
2 - 323*x - 16*x^3)^(5^(1/x))