3.78.54 \(\int \frac {512 x^2-128 x^3+(1536 x^2-128 x^3) \log (x)+\frac {e^{5-x} (32 x^2+(160 x^2+64 x^3) \log (x))}{x}}{4096+\frac {e^{15-3 x}}{x^3}+\frac {e^{10-2 x} (48-12 x)}{x^2}-3072 x+768 x^2-64 x^3+\frac {e^{5-x} (768-384 x+48 x^2)}{x}} \, dx\)

Optimal. Leaf size=28 \[ \frac {2 x^3 \log (x)}{\left (4+\frac {e^{5-x}}{4 x}-x\right )^2} \]

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Rubi [F]  time = 20.75, 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 {512 x^2-128 x^3+\left (1536 x^2-128 x^3\right ) \log (x)+\frac {e^{5-x} \left (32 x^2+\left (160 x^2+64 x^3\right ) \log (x)\right )}{x}}{4096+\frac {e^{15-3 x}}{x^3}+\frac {e^{10-2 x} (48-12 x)}{x^2}-3072 x+768 x^2-64 x^3+\frac {e^{5-x} \left (768-384 x+48 x^2\right )}{x}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(512*x^2 - 128*x^3 + (1536*x^2 - 128*x^3)*Log[x] + (E^(5 - x)*(32*x^2 + (160*x^2 + 64*x^3)*Log[x]))/x)/(40
96 + E^(15 - 3*x)/x^3 + (E^(10 - 2*x)*(48 - 12*x))/x^2 - 3072*x + 768*x^2 - 64*x^3 + (E^(5 - x)*(768 - 384*x +
48*x^2))/x),x]

[Out]

-65536*Log[x]*Defer[Int][E^(2*x)/((-4 + x)*(E^5 - 4*E^x*(-4 + x)*x)^2), x] - 4096*Log[x]*Defer[Int][(E^(2*x)*x
)/(E^5 - 4*E^x*(-4 + x)*x)^2, x] - 1024*Log[x]*Defer[Int][(E^(2*x)*x^2)/(E^5 - 4*E^x*(-4 + x)*x)^2, x] - 256*L
og[x]*Defer[Int][(E^(2*x)*x^3)/(E^5 - 4*E^x*(-4 + x)*x)^2, x] + 32*Defer[Int][(E^(2*x)*x^4)/(E^5 - 4*E^x*(-4 +
x)*x)^2, x] + 32*Log[x]*Defer[Int][(E^(2*x)*x^4)/(E^5 - 4*E^x*(-4 + x)*x)^2, x] + 16384*Log[x]*Defer[Int][E^(
5 + 2*x)/(E^5 + 16*E^x*x - 4*E^x*x^2)^3, x] - 16384*Log[x]*Defer[Int][E^(2*x)/(E^5 + 16*E^x*x - 4*E^x*x^2)^2,
x] - 65536*Log[x]*Defer[Int][E^(5 + 2*x)/((-4 + x)*(-E^5 - 16*E^x*x + 4*E^x*x^2)^3), x] - 4096*Log[x]*Defer[In
t][(E^(5 + 2*x)*x)/(-E^5 - 16*E^x*x + 4*E^x*x^2)^3, x] - 1024*Log[x]*Defer[Int][(E^(5 + 2*x)*x^2)/(-E^5 - 16*E
^x*x + 4*E^x*x^2)^3, x] - 256*Log[x]*Defer[Int][(E^(5 + 2*x)*x^3)/(-E^5 - 16*E^x*x + 4*E^x*x^2)^3, x] - 128*Lo
g[x]*Defer[Int][(E^(5 + 2*x)*x^4)/(-E^5 - 16*E^x*x + 4*E^x*x^2)^3, x] - 64*Log[x]*Defer[Int][(E^(5 + 2*x)*x^5)
/(-E^5 - 16*E^x*x + 4*E^x*x^2)^3, x] - 16384*Defer[Int][Defer[Int][E^(5 + 2*x)/(E^5 - 4*E^x*(-4 + x)*x)^3, x]/
x, x] + 4096*Defer[Int][Defer[Int][-((E^(5 + 2*x)*x)/(E^5 - 4*E^x*(-4 + x)*x)^3), x]/x, x] + 1024*Defer[Int][D
efer[Int][-((E^(5 + 2*x)*x^2)/(E^5 - 4*E^x*(-4 + x)*x)^3), x]/x, x] + 256*Defer[Int][Defer[Int][-((E^(5 + 2*x)
*x^3)/(E^5 - 4*E^x*(-4 + x)*x)^3), x]/x, x] + 128*Defer[Int][Defer[Int][-((E^(5 + 2*x)*x^4)/(E^5 - 4*E^x*(-4 +
x)*x)^3), x]/x, x] + 64*Defer[Int][Defer[Int][-((E^(5 + 2*x)*x^5)/(E^5 - 4*E^x*(-4 + x)*x)^3), x]/x, x] + 163
84*Defer[Int][Defer[Int][E^(2*x)/(E^5 - 4*E^x*(-4 + x)*x)^2, x]/x, x] + 65536*Defer[Int][Defer[Int][E^(2*x)/((
-4 + x)*(E^5 - 4*E^x*(-4 + x)*x)^2), x]/x, x] + 4096*Defer[Int][Defer[Int][(E^(2*x)*x)/(E^5 - 4*E^x*(-4 + x)*x
)^2, x]/x, x] + 1024*Defer[Int][Defer[Int][(E^(2*x)*x^2)/(E^5 - 4*E^x*(-4 + x)*x)^2, x]/x, x] + 256*Defer[Int]
[Defer[Int][(E^(2*x)*x^3)/(E^5 - 4*E^x*(-4 + x)*x)^2, x]/x, x] - 32*Defer[Int][Defer[Int][(E^(2*x)*x^4)/(E^5 -
4*E^x*(-4 + x)*x)^2, x]/x, x] + 65536*Defer[Int][Defer[Int][E^(5 + 2*x)/((-4 + x)*(-E^5 + 4*E^x*(-4 + x)*x)^3
), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32 e^{2 x} x^4 \left (e^5-4 e^x (-4+x) x-4 e^x (-12+x) x \log (x)+e^5 (5+2 x) \log (x)\right )}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx\\ &=32 \int \frac {e^{2 x} x^4 \left (e^5-4 e^x (-4+x) x-4 e^x (-12+x) x \log (x)+e^5 (5+2 x) \log (x)\right )}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx\\ &=32 \int \left (\frac {2 e^{5+2 x} x^4 \left (-4-2 x+x^2\right ) \log (x)}{(-4+x) \left (e^5+16 e^x x-4 e^x x^2\right )^3}+\frac {e^{2 x} x^4 (-4+x-12 \log (x)+x \log (x))}{(-4+x) \left (-e^5-16 e^x x+4 e^x x^2\right )^2}\right ) \, dx\\ &=32 \int \frac {e^{2 x} x^4 (-4+x-12 \log (x)+x \log (x))}{(-4+x) \left (-e^5-16 e^x x+4 e^x x^2\right )^2} \, dx+64 \int \frac {e^{5+2 x} x^4 \left (-4-2 x+x^2\right ) \log (x)}{(-4+x) \left (e^5+16 e^x x-4 e^x x^2\right )^3} \, dx\\ &=32 \int \left (\frac {64 e^{2 x} (-4+x-12 \log (x)+x \log (x))}{\left (e^5+16 e^x x-4 e^x x^2\right )^2}+\frac {256 e^{2 x} (-4+x-12 \log (x)+x \log (x))}{(-4+x) \left (-e^5-16 e^x x+4 e^x x^2\right )^2}+\frac {16 e^{2 x} x (-4+x-12 \log (x)+x \log (x))}{\left (-e^5-16 e^x x+4 e^x x^2\right )^2}+\frac {4 e^{2 x} x^2 (-4+x-12 \log (x)+x \log (x))}{\left (-e^5-16 e^x x+4 e^x x^2\right )^2}+\frac {e^{2 x} x^3 (-4+x-12 \log (x)+x \log (x))}{\left (-e^5-16 e^x x+4 e^x x^2\right )^2}\right ) \, dx-64 \int \frac {256 \int \frac {e^{5+2 x}}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx-64 \int -\frac {e^{5+2 x} x}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx-16 \int -\frac {e^{5+2 x} x^2}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx-4 \int -\frac {e^{5+2 x} x^3}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx-2 \int -\frac {e^{5+2 x} x^4}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx-\int -\frac {e^{5+2 x} x^5}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx-1024 \int \frac {e^{5+2 x}}{(-4+x) \left (-e^5+4 e^x (-4+x) x\right )^3} \, dx}{x} \, dx-(64 \log (x)) \int \frac {e^{5+2 x} x^5}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx-(128 \log (x)) \int \frac {e^{5+2 x} x^4}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx-(256 \log (x)) \int \frac {e^{5+2 x} x^3}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx-(1024 \log (x)) \int \frac {e^{5+2 x} x^2}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx-(4096 \log (x)) \int \frac {e^{5+2 x} x}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx+(16384 \log (x)) \int \frac {e^{5+2 x}}{\left (e^5+16 e^x x-4 e^x x^2\right )^3} \, dx-(65536 \log (x)) \int \frac {e^{5+2 x}}{(-4+x) \left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx\\ &=32 \int \frac {e^{2 x} x^3 (-4+x-12 \log (x)+x \log (x))}{\left (-e^5-16 e^x x+4 e^x x^2\right )^2} \, dx-64 \int \left (\frac {256 \int \frac {e^{5+2 x}}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx+64 \int \frac {e^{5+2 x} x}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx+16 \int \frac {e^{5+2 x} x^2}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx+4 \int \frac {e^{5+2 x} x^3}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx+2 \int \frac {e^{5+2 x} x^4}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx+\int \frac {e^{5+2 x} x^5}{\left (e^5-4 e^x (-4+x) x\right )^3} \, dx}{x}-\frac {1024 \int \frac {e^{5+2 x}}{(-4+x) \left (-e^5+4 e^x (-4+x) x\right )^3} \, dx}{x}\right ) \, dx+128 \int \frac {e^{2 x} x^2 (-4+x-12 \log (x)+x \log (x))}{\left (-e^5-16 e^x x+4 e^x x^2\right )^2} \, dx+512 \int \frac {e^{2 x} x (-4+x-12 \log (x)+x \log (x))}{\left (-e^5-16 e^x x+4 e^x x^2\right )^2} \, dx+2048 \int \frac {e^{2 x} (-4+x-12 \log (x)+x \log (x))}{\left (e^5+16 e^x x-4 e^x x^2\right )^2} \, dx+8192 \int \frac {e^{2 x} (-4+x-12 \log (x)+x \log (x))}{(-4+x) \left (-e^5-16 e^x x+4 e^x x^2\right )^2} \, dx-(64 \log (x)) \int \frac {e^{5+2 x} x^5}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx-(128 \log (x)) \int \frac {e^{5+2 x} x^4}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx-(256 \log (x)) \int \frac {e^{5+2 x} x^3}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx-(1024 \log (x)) \int \frac {e^{5+2 x} x^2}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx-(4096 \log (x)) \int \frac {e^{5+2 x} x}{\left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx+(16384 \log (x)) \int \frac {e^{5+2 x}}{\left (e^5+16 e^x x-4 e^x x^2\right )^3} \, dx-(65536 \log (x)) \int \frac {e^{5+2 x}}{(-4+x) \left (-e^5-16 e^x x+4 e^x x^2\right )^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 4.65, size = 27, normalized size = 0.96 \begin {gather*} \frac {32 e^{2 x} x^5 \log (x)}{\left (e^5-4 e^x (-4+x) x\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(512*x^2 - 128*x^3 + (1536*x^2 - 128*x^3)*Log[x] + (E^(5 - x)*(32*x^2 + (160*x^2 + 64*x^3)*Log[x]))/
x)/(4096 + E^(15 - 3*x)/x^3 + (E^(10 - 2*x)*(48 - 12*x))/x^2 - 3072*x + 768*x^2 - 64*x^3 + (E^(5 - x)*(768 - 3
84*x + 48*x^2))/x),x]

[Out]

(32*E^(2*x)*x^5*Log[x])/(E^5 - 4*E^x*(-4 + x)*x)^2

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fricas [A]  time = 0.75, size = 44, normalized size = 1.57 \begin {gather*} \frac {32 \, x^{3} \log \relax (x)}{16 \, x^{2} - 8 \, {\left (x - 4\right )} e^{\left (-x - \log \relax (x) + 5\right )} - 128 \, x + e^{\left (-2 \, x - 2 \, \log \relax (x) + 10\right )} + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^3+160*x^2)*log(x)+32*x^2)*exp(5-log(x)-x)+(-128*x^3+1536*x^2)*log(x)-128*x^3+512*x^2)/(exp(5
-log(x)-x)^3+(-12*x+48)*exp(5-log(x)-x)^2+(48*x^2-384*x+768)*exp(5-log(x)-x)-64*x^3+768*x^2-3072*x+4096),x, al
gorithm="fricas")

[Out]

32*x^3*log(x)/(16*x^2 - 8*(x - 4)*e^(-x - log(x) + 5) - 128*x + e^(-2*x - 2*log(x) + 10) + 256)

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giac [B]  time = 0.31, size = 1012, normalized size = 36.14 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^3+160*x^2)*log(x)+32*x^2)*exp(5-log(x)-x)+(-128*x^3+1536*x^2)*log(x)-128*x^3+512*x^2)/(exp(5
-log(x)-x)^3+(-12*x+48)*exp(5-log(x)-x)^2+(48*x^2-384*x+768)*exp(5-log(x)-x)-64*x^3+768*x^2-3072*x+4096),x, al
gorithm="giac")

[Out]

(512*x^15*e^(2*x)*log(x) - 7168*x^14*e^(2*x)*log(x) - 768*x^14*e^(2*x) + 32768*x^13*e^(2*x)*log(x) - 256*x^13*
e^(x + 5)*log(x) + 16896*x^13*e^(2*x) - 28672*x^12*e^(2*x)*log(x) + 2560*x^12*e^(x + 5)*log(x) - 147456*x^12*e
^(2*x) + 768*x^12*e^(x + 5) + 32*x^11*e^10*log(x) - 163840*x^11*e^(2*x)*log(x) - 6144*x^11*e^(x + 5)*log(x) +
608256*x^11*e^(2*x) - 13824*x^11*e^(x + 5) - 192*x^10*e^10*log(x) + 278528*x^10*e^(2*x)*log(x) - 10240*x^10*e^
(x + 5)*log(x) - 288*x^10*e^10 - 884736*x^10*e^(2*x) + 92160*x^10*e^(x + 5) + 360448*x^9*e^(2*x)*log(x) + 4096
0*x^9*e^(x + 5)*log(x) + 4032*x^9*e^10 - 1695744*x^9*e^(2*x) - 239616*x^9*e^(x + 5) + 1280*x^8*e^10*log(x) - 5
24288*x^8*e^(2*x)*log(x) + 24576*x^8*e^(x + 5)*log(x) - 18432*x^8*e^10 + 6733824*x^8*e^(2*x) - 73728*x^8*e^(x
+ 5) + 48*x^8*e^(-x + 15) - 524288*x^7*e^(2*x)*log(x) - 81920*x^7*e^(x + 5)*log(x) + 16128*x^7*e^10 - 1572864*
x^7*e^(2*x) + 1400832*x^7*e^(x + 5) - 480*x^7*e^(-x + 15) - 3072*x^6*e^10*log(x) - 65536*x^6*e^(x + 5)*log(x)
+ 92160*x^6*e^10 - 14155776*x^6*e^(2*x) - 1130496*x^6*e^(x + 5) + 1152*x^6*e^(-x + 15) - 3*x^6*e^(-2*x + 20) -
2048*x^5*e^10*log(x) - 156672*x^5*e^10 + 6291456*x^5*e^(2*x) - 2949120*x^5*e^(x + 5) + 1920*x^5*e^(-x + 15) +
18*x^5*e^(-2*x + 20) - 202752*x^4*e^10 + 12582912*x^4*e^(2*x) + 2359296*x^4*e^(x + 5) - 7680*x^4*e^(-x + 15)
+ 294912*x^3*e^10 + 3145728*x^3*e^(x + 5) - 4608*x^3*e^(-x + 15) - 120*x^3*e^(-2*x + 20) + 294912*x^2*e^10 + 1
5360*x^2*e^(-x + 15) + 12288*x*e^(-x + 15) + 288*x*e^(-2*x + 20) + 192*e^(-2*x + 20))/(256*x^14*e^(2*x) - 5632
*x^13*e^(2*x) + 49152*x^12*e^(2*x) - 256*x^12*e^(x + 5) - 202752*x^11*e^(2*x) + 4608*x^11*e^(x + 5) + 96*x^10*
e^10 + 294912*x^10*e^(2*x) - 30720*x^10*e^(x + 5) - 1344*x^9*e^10 + 565248*x^9*e^(2*x) + 79872*x^9*e^(x + 5) +
6144*x^8*e^10 - 2244608*x^8*e^(2*x) + 24576*x^8*e^(x + 5) - 16*x^8*e^(-x + 15) - 5376*x^7*e^10 + 524288*x^7*e
^(2*x) - 466944*x^7*e^(x + 5) + 160*x^7*e^(-x + 15) - 30720*x^6*e^10 + 4718592*x^6*e^(2*x) + 376832*x^6*e^(x +
5) - 384*x^6*e^(-x + 15) + x^6*e^(-2*x + 20) + 52224*x^5*e^10 - 2097152*x^5*e^(2*x) + 983040*x^5*e^(x + 5) -
640*x^5*e^(-x + 15) - 6*x^5*e^(-2*x + 20) + 67584*x^4*e^10 - 4194304*x^4*e^(2*x) - 786432*x^4*e^(x + 5) + 2560
*x^4*e^(-x + 15) - 98304*x^3*e^10 - 1048576*x^3*e^(x + 5) + 1536*x^3*e^(-x + 15) + 40*x^3*e^(-2*x + 20) - 9830
4*x^2*e^10 - 5120*x^2*e^(-x + 15) - 4096*x*e^(-x + 15) - 96*x*e^(-2*x + 20) - 64*e^(-2*x + 20))

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maple [A]  time = 0.04, size = 26, normalized size = 0.93

method	result	size
risch	\(\frac {32 x^{3} \ln \relax (x )}{\left (4 x -\frac {{\mathrm e}^{5-x}}{x}-16\right )^{2}}\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((64*x^3+160*x^2)*ln(x)+32*x^2)*exp(5-ln(x)-x)+(-128*x^3+1536*x^2)*ln(x)-128*x^3+512*x^2)/(exp(5-ln(x)-x)
^3+(-12*x+48)*exp(5-ln(x)-x)^2+(48*x^2-384*x+768)*exp(5-ln(x)-x)-64*x^3+768*x^2-3072*x+4096),x,method=_RETURNV
ERBOSE)

[Out]

32*x^3*ln(x)/(4*x-1/x*exp(5-x)-16)^2

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maxima [A]  time = 0.47, size = 52, normalized size = 1.86 \begin {gather*} \frac {32 \, x^{5} e^{\left (2 \, x\right )} \log \relax (x)}{16 \, {\left (x^{4} - 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (2 \, x\right )} - 8 \, {\left (x^{2} e^{5} - 4 \, x e^{5}\right )} e^{x} + e^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^3+160*x^2)*log(x)+32*x^2)*exp(5-log(x)-x)+(-128*x^3+1536*x^2)*log(x)-128*x^3+512*x^2)/(exp(5
-log(x)-x)^3+(-12*x+48)*exp(5-log(x)-x)^2+(48*x^2-384*x+768)*exp(5-log(x)-x)-64*x^3+768*x^2-3072*x+4096),x, al
gorithm="maxima")

[Out]

32*x^5*e^(2*x)*log(x)/(16*(x^4 - 8*x^3 + 16*x^2)*e^(2*x) - 8*(x^2*e^5 - 4*x*e^5)*e^x + e^10)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \relax (x)\,\left (1536\,x^2-128\,x^3\right )+512\,x^2-128\,x^3+{\mathrm {e}}^{5-\ln \relax (x)-x}\,\left (\ln \relax (x)\,\left (64\,x^3+160\,x^2\right )+32\,x^2\right )}{{\mathrm {e}}^{15-3\,\ln \relax (x)-3\,x}-3072\,x-{\mathrm {e}}^{10-2\,\ln \relax (x)-2\,x}\,\left (12\,x-48\right )+{\mathrm {e}}^{5-\ln \relax (x)-x}\,\left (48\,x^2-384\,x+768\right )+768\,x^2-64\,x^3+4096} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(1536*x^2 - 128*x^3) + 512*x^2 - 128*x^3 + exp(5 - log(x) - x)*(log(x)*(160*x^2 + 64*x^3) + 32*x^2
))/(exp(15 - 3*log(x) - 3*x) - 3072*x - exp(10 - 2*log(x) - 2*x)*(12*x - 48) + exp(5 - log(x) - x)*(48*x^2 - 3
84*x + 768) + 768*x^2 - 64*x^3 + 4096),x)

[Out]

int((log(x)*(1536*x^2 - 128*x^3) + 512*x^2 - 128*x^3 + exp(5 - log(x) - x)*(log(x)*(160*x^2 + 64*x^3) + 32*x^2
))/(exp(15 - 3*log(x) - 3*x) - 3072*x - exp(10 - 2*log(x) - 2*x)*(12*x - 48) + exp(5 - log(x) - x)*(48*x^2 - 3
84*x + 768) + 768*x^2 - 64*x^3 + 4096), x)

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sympy [B]  time = 0.40, size = 42, normalized size = 1.50 \begin {gather*} \frac {32 x^{5} \log {\relax (x )}}{16 x^{4} - 128 x^{3} + 256 x^{2} + \left (- 8 x^{2} + 32 x\right ) e^{5 - x} + e^{10 - 2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x**3+160*x**2)*ln(x)+32*x**2)*exp(5-ln(x)-x)+(-128*x**3+1536*x**2)*ln(x)-128*x**3+512*x**2)/(e
xp(5-ln(x)-x)**3+(-12*x+48)*exp(5-ln(x)-x)**2+(48*x**2-384*x+768)*exp(5-ln(x)-x)-64*x**3+768*x**2-3072*x+4096)
,x)

[Out]

32*x**5*log(x)/(16*x**4 - 128*x**3 + 256*x**2 + (-8*x**2 + 32*x)*exp(5 - x) + exp(10 - 2*x))

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