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

Optimal. Leaf size=31 \[ \frac {\left (\left (-3+16 \left (5-(5-x)^2\right )\right ) x\right )^{2-5^{\frac {1}{x}}}}{x} \]

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Rubi [F]  time = 12.27, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\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 \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 34, normalized size = 1.10 \begin {gather*} 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 \end {gather*}

Antiderivative was successfully verified.

[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)

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fricas [A]  time = 0.64, size = 28, normalized size = 0.90 \begin {gather*} \frac {{\left (-16 \, x^{3} + 160 \, x^{2} - 323 \, x\right )}^{-5^{\left (\frac {1}{x}\right )} + 2}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left ({\left (16 \, x^{2} - 160 \, x + 323\right )} 5^{\left (\frac {1}{x}\right )} \log \relax (5) \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maple [C]  time = 0.13, size = 162, normalized size = 5.23

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

Verification of antiderivative is not currently implemented for this CAS.

[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]

1/x*exp(-1/2*(5^(1/x)-2)*(I*Pi*csgn(I*x*(x^2-10*x+323/16))^3+I*Pi*csgn(I*x*(x^2-10*x+323/16))^2*csgn(I*x)+I*Pi
*csgn(I*x*(x^2-10*x+323/16))^2*csgn(I*(x^2-10*x+323/16))-I*Pi*csgn(I*x*(x^2-10*x+323/16))*csgn(I*x)*csgn(I*(x^
2-10*x+323/16))-2*I*Pi*csgn(I*x*(x^2-10*x+323/16))^2+2*I*Pi+2*ln(x)+2*ln(x^2-10*x+323/16)))

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maxima [B]  time = 0.50, size = 54, normalized size = 1.74 \begin {gather*} {\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 \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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mupad [B]  time = 2.47, size = 134, normalized size = 4.32 \begin {gather*} \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}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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sympy [A]  time = 1.23, size = 26, normalized size = 0.84 \begin {gather*} \frac {e^{\left (2 - e^{\frac {\log {\relax (5 )}}{x}}\right ) \log {\left (- 16 x^{3} + 160 x^{2} - 323 x \right )}}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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