3.50.11 \(\int \frac {e^{4 x} (-256+64 x)+(16-5 x) \log (2)+(-256+64 x) \log ^2(2)+e^{2 x} (-16+37 x-8 x^2+(512-128 x) \log (2))+(e^{4 x} (-128+32 x)+(4-x) \log (2)+(-128+32 x) \log ^2(2)+e^{2 x} (-4+9 x-2 x^2+(256-64 x) \log (2))) \log (-\frac {4}{-4+x})+(e^{4 x} (-16+4 x)+e^{2 x} (32-8 x) \log (2)+(-16+4 x) \log ^2(2)) \log ^2(-\frac {4}{-4+x})}{e^{4 x} (-256-192 x+64 x^2)+(16 x-4 x^2) \log (2)+(-256-192 x+64 x^2) \log ^2(2)+e^{2 x} (-16 x+4 x^2+(512+384 x-128 x^2) \log (2))+(e^{4 x} (-128-96 x+32 x^2)+(4 x-x^2) \log (2)+(-128-96 x+32 x^2) \log ^2(2)+e^{2 x} (-4 x+x^2+(256+192 x-64 x^2) \log (2))) \log (-\frac {4}{-4+x})+(e^{4 x} (-16-12 x+4 x^2)+e^{2 x} (32+24 x-8 x^2) \log (2)+(-16-12 x+4 x^2) \log ^2(2)) \log ^2(-\frac {4}{-4+x})} \, dx\)
Optimal. Leaf size=37 \[ \log \left (1+x+\frac {x}{4 \left (e^{2 x}-\log (2)\right ) \left (4+\log \left (1+\frac {x}{4-x}\right )\right )}\right ) \]
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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(E^(4*x)*(-256 + 64*x) + (16 - 5*x)*Log[2] + (-256 + 64*x)*Log[2]^2 + E^(2*x)*(-16 + 37*x - 8*x^2 + (512 -
128*x)*Log[2]) + (E^(4*x)*(-128 + 32*x) + (4 - x)*Log[2] + (-128 + 32*x)*Log[2]^2 + E^(2*x)*(-4 + 9*x - 2*x^2
+ (256 - 64*x)*Log[2]))*Log[-4/(-4 + x)] + (E^(4*x)*(-16 + 4*x) + E^(2*x)*(32 - 8*x)*Log[2] + (-16 + 4*x)*Log
[2]^2)*Log[-4/(-4 + x)]^2)/(E^(4*x)*(-256 - 192*x + 64*x^2) + (16*x - 4*x^2)*Log[2] + (-256 - 192*x + 64*x^2)*
Log[2]^2 + E^(2*x)*(-16*x + 4*x^2 + (512 + 384*x - 128*x^2)*Log[2]) + (E^(4*x)*(-128 - 96*x + 32*x^2) + (4*x -
x^2)*Log[2] + (-128 - 96*x + 32*x^2)*Log[2]^2 + E^(2*x)*(-4*x + x^2 + (256 + 192*x - 64*x^2)*Log[2]))*Log[-4/
(-4 + x)] + (E^(4*x)*(-16 - 12*x + 4*x^2) + E^(2*x)*(32 + 24*x - 8*x^2)*Log[2] + (-16 - 12*x + 4*x^2)*Log[2]^2
)*Log[-4/(-4 + x)]^2),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [B] time = 0.45, size = 118, normalized size = 3.19 \begin {gather*} \log (1+x)-\log \left ((1+x) \left (e^{2 x}-\log (2)\right )\right )-\log \left (4+\log \left (-\frac {4}{-4+x}\right )\right )+\log \left (16 e^{2 x}+x+16 e^{2 x} x-16 \log (2)-16 x \log (2)+4 e^{2 x} \log \left (-\frac {4}{-4+x}\right )+4 e^{2 x} x \log \left (-\frac {4}{-4+x}\right )-4 \log (2) \log \left (-\frac {4}{-4+x}\right )-4 x \log (2) \log \left (-\frac {4}{-4+x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^(4*x)*(-256 + 64*x) + (16 - 5*x)*Log[2] + (-256 + 64*x)*Log[2]^2 + E^(2*x)*(-16 + 37*x - 8*x^2 +
(512 - 128*x)*Log[2]) + (E^(4*x)*(-128 + 32*x) + (4 - x)*Log[2] + (-128 + 32*x)*Log[2]^2 + E^(2*x)*(-4 + 9*x -
2*x^2 + (256 - 64*x)*Log[2]))*Log[-4/(-4 + x)] + (E^(4*x)*(-16 + 4*x) + E^(2*x)*(32 - 8*x)*Log[2] + (-16 + 4*
x)*Log[2]^2)*Log[-4/(-4 + x)]^2)/(E^(4*x)*(-256 - 192*x + 64*x^2) + (16*x - 4*x^2)*Log[2] + (-256 - 192*x + 64
*x^2)*Log[2]^2 + E^(2*x)*(-16*x + 4*x^2 + (512 + 384*x - 128*x^2)*Log[2]) + (E^(4*x)*(-128 - 96*x + 32*x^2) +
(4*x - x^2)*Log[2] + (-128 - 96*x + 32*x^2)*Log[2]^2 + E^(2*x)*(-4*x + x^2 + (256 + 192*x - 64*x^2)*Log[2]))*L
og[-4/(-4 + x)] + (E^(4*x)*(-16 - 12*x + 4*x^2) + E^(2*x)*(32 + 24*x - 8*x^2)*Log[2] + (-16 - 12*x + 4*x^2)*Lo
g[2]^2)*Log[-4/(-4 + x)]^2),x]
[Out]
Log[1 + x] - Log[(1 + x)*(E^(2*x) - Log[2])] - Log[4 + Log[-4/(-4 + x)]] + Log[16*E^(2*x) + x + 16*E^(2*x)*x -
16*Log[2] - 16*x*Log[2] + 4*E^(2*x)*Log[-4/(-4 + x)] + 4*E^(2*x)*x*Log[-4/(-4 + x)] - 4*Log[2]*Log[-4/(-4 + x
)] - 4*x*Log[2]*Log[-4/(-4 + x)]]
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fricas [B] time = 0.90, size = 82, normalized size = 2.22 \begin {gather*} \log \left (x + 1\right ) + \log \left (\frac {16 \, {\left (x + 1\right )} e^{\left (2 \, x\right )} - 16 \, {\left (x + 1\right )} \log \relax (2) + 4 \, {\left ({\left (x + 1\right )} e^{\left (2 \, x\right )} - {\left (x + 1\right )} \log \relax (2)\right )} \log \left (-\frac {4}{x - 4}\right ) + x}{{\left (x + 1\right )} e^{\left (2 \, x\right )} - {\left (x + 1\right )} \log \relax (2)}\right ) - \log \left (\log \left (-\frac {4}{x - 4}\right ) + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x-16)*exp(x)^4+(-8*x+32)*log(2)*exp(x)^2+(4*x-16)*log(2)^2)*log(-4/(x-4))^2+((32*x-128)*exp(x)^
4+((-64*x+256)*log(2)-2*x^2+9*x-4)*exp(x)^2+(32*x-128)*log(2)^2+(-x+4)*log(2))*log(-4/(x-4))+(64*x-256)*exp(x)
^4+((-128*x+512)*log(2)-8*x^2+37*x-16)*exp(x)^2+(64*x-256)*log(2)^2+(-5*x+16)*log(2))/(((4*x^2-12*x-16)*exp(x)
^4+(-8*x^2+24*x+32)*log(2)*exp(x)^2+(4*x^2-12*x-16)*log(2)^2)*log(-4/(x-4))^2+((32*x^2-96*x-128)*exp(x)^4+((-6
4*x^2+192*x+256)*log(2)+x^2-4*x)*exp(x)^2+(32*x^2-96*x-128)*log(2)^2+(-x^2+4*x)*log(2))*log(-4/(x-4))+(64*x^2-
192*x-256)*exp(x)^4+((-128*x^2+384*x+512)*log(2)+4*x^2-16*x)*exp(x)^2+(64*x^2-192*x-256)*log(2)^2+(-4*x^2+16*x
)*log(2)),x, algorithm="fricas")
[Out]
log(x + 1) + log((16*(x + 1)*e^(2*x) - 16*(x + 1)*log(2) + 4*((x + 1)*e^(2*x) - (x + 1)*log(2))*log(-4/(x - 4)
) + x)/((x + 1)*e^(2*x) - (x + 1)*log(2))) - log(log(-4/(x - 4)) + 4)
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giac [B] time = 1.82, size = 1010, normalized size = 27.30 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x-16)*exp(x)^4+(-8*x+32)*log(2)*exp(x)^2+(4*x-16)*log(2)^2)*log(-4/(x-4))^2+((32*x-128)*exp(x)^
4+((-64*x+256)*log(2)-2*x^2+9*x-4)*exp(x)^2+(32*x-128)*log(2)^2+(-x+4)*log(2))*log(-4/(x-4))+(64*x-256)*exp(x)
^4+((-128*x+512)*log(2)-8*x^2+37*x-16)*exp(x)^2+(64*x-256)*log(2)^2+(-5*x+16)*log(2))/(((4*x^2-12*x-16)*exp(x)
^4+(-8*x^2+24*x+32)*log(2)*exp(x)^2+(4*x^2-12*x-16)*log(2)^2)*log(-4/(x-4))^2+((32*x^2-96*x-128)*exp(x)^4+((-6
4*x^2+192*x+256)*log(2)+x^2-4*x)*exp(x)^2+(32*x^2-96*x-128)*log(2)^2+(-x^2+4*x)*log(2))*log(-4/(x-4))+(64*x^2-
192*x-256)*exp(x)^4+((-128*x^2+384*x+512)*log(2)+4*x^2-16*x)*exp(x)^2+(64*x^2-192*x-256)*log(2)^2+(-4*x^2+16*x
)*log(2)),x, algorithm="giac")
[Out]
1/2*log(-16*pi^2*x^2*e^(2*x)*log(2)*sgn(x - 4) + 8*pi^2*x^2*log(2)^2*sgn(x - 4) - 16*pi^2*x^2*e^(2*x)*log(2) +
8*pi^2*x^2*log(2)^2 - 128*x^2*e^(2*x)*log(2)^3 + 64*x^2*log(2)^4 + 128*x^2*e^(2*x)*log(2)^2*log(abs(x - 4)) -
64*x^2*log(2)^3*log(abs(x - 4)) - 32*x^2*e^(2*x)*log(2)*log(abs(x - 4))^2 + 16*x^2*log(2)^2*log(abs(x - 4))^2
+ 8*pi^2*x^2*e^(4*x)*sgn(x - 4) - 32*pi^2*x*e^(2*x)*log(2)*sgn(x - 4) + 16*pi^2*x*log(2)^2*sgn(x - 4) + 8*pi^
2*x^2*e^(4*x) - 32*pi^2*x*e^(2*x)*log(2) + 16*pi^2*x*log(2)^2 + 64*x^2*e^(4*x)*log(2)^2 - 512*x^2*e^(2*x)*log(
2)^2 + 256*x^2*log(2)^3 - 256*x*e^(2*x)*log(2)^3 + 128*x*log(2)^4 - 64*x^2*e^(4*x)*log(2)*log(abs(x - 4)) + 25
6*x^2*e^(2*x)*log(2)*log(abs(x - 4)) - 128*x^2*log(2)^2*log(abs(x - 4)) + 256*x*e^(2*x)*log(2)^2*log(abs(x - 4
)) - 128*x*log(2)^3*log(abs(x - 4)) + 16*x^2*e^(4*x)*log(abs(x - 4))^2 - 64*x*e^(2*x)*log(2)*log(abs(x - 4))^2
+ 32*x*log(2)^2*log(abs(x - 4))^2 + 16*pi^2*x*e^(4*x)*sgn(x - 4) - 16*pi^2*e^(2*x)*log(2)*sgn(x - 4) + 8*pi^2
*log(2)^2*sgn(x - 4) + 16*pi^2*x*e^(4*x) + 256*x^2*e^(4*x)*log(2) - 16*pi^2*e^(2*x)*log(2) - 496*x^2*e^(2*x)*l
og(2) + 8*pi^2*log(2)^2 + 240*x^2*log(2)^2 + 128*x*e^(4*x)*log(2)^2 - 1024*x*e^(2*x)*log(2)^2 + 512*x*log(2)^3
- 128*e^(2*x)*log(2)^3 + 64*log(2)^4 - 128*x^2*e^(4*x)*log(abs(x - 4)) - 8*x^2*e^(2*x)*log(abs(x - 4)) + 8*x^
2*log(2)*log(abs(x - 4)) - 128*x*e^(4*x)*log(2)*log(abs(x - 4)) + 512*x*e^(2*x)*log(2)*log(abs(x - 4)) - 256*x
*log(2)^2*log(abs(x - 4)) + 128*e^(2*x)*log(2)^2*log(abs(x - 4)) - 64*log(2)^3*log(abs(x - 4)) + 32*x*e^(4*x)*
log(abs(x - 4))^2 - 32*e^(2*x)*log(2)*log(abs(x - 4))^2 + 16*log(2)^2*log(abs(x - 4))^2 + 8*pi^2*e^(4*x)*sgn(x
- 4) + 8*pi^2*e^(4*x) + 256*x^2*e^(4*x) + 32*x^2*e^(2*x) - 32*x^2*log(2) + 512*x*e^(4*x)*log(2) - 1008*x*e^(2
*x)*log(2) + 496*x*log(2)^2 + 64*e^(4*x)*log(2)^2 - 512*e^(2*x)*log(2)^2 + 256*log(2)^3 - 256*x*e^(4*x)*log(ab
s(x - 4)) - 8*x*e^(2*x)*log(abs(x - 4)) + 8*x*log(2)*log(abs(x - 4)) - 64*e^(4*x)*log(2)*log(abs(x - 4)) + 256
*e^(2*x)*log(2)*log(abs(x - 4)) - 128*log(2)^2*log(abs(x - 4)) + 16*e^(4*x)*log(abs(x - 4))^2 + x^2 + 512*x*e^
(4*x) + 32*x*e^(2*x) - 32*x*log(2) + 256*e^(4*x)*log(2) - 512*e^(2*x)*log(2) + 256*log(2)^2 - 128*e^(4*x)*log(
abs(x - 4)) + 256*e^(4*x)) - 1/2*log(1/2*pi^2*sgn(x - 4) + 1/2*pi^2 + 4*log(2)^2 - 4*log(2)*log(abs(x - 4)) +
log(abs(x - 4))^2 + 16*log(2) - 8*log(abs(x - 4)) + 16) - log(abs(e^(2*x) - log(2)))
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maple [C] time = 1.05, size = 318, normalized size = 8.59
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result |
size |
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| risch |
\(\ln \left (x +1\right )+\ln \left (\ln \left (x -4\right )-\frac {i \left (4 \pi \ln \relax (2) x -4 \pi x \,{\mathrm e}^{2 x}+16 i x \,{\mathrm e}^{2 x}-16 i x \ln \relax (2)+8 i \ln \relax (2) x \,{\mathrm e}^{2 x}-4 \pi x \mathrm {csgn}\left (\frac {i}{x -4}\right )^{3} {\mathrm e}^{2 x}+4 \pi \ln \relax (2) x \mathrm {csgn}\left (\frac {i}{x -4}\right )^{3}+8 i {\mathrm e}^{2 x} \ln \relax (2)-8 i \ln \relax (2)^{2}+i x -8 i \ln \relax (2)^{2} x +16 i {\mathrm e}^{2 x}+4 \ln \relax (2) \pi \mathrm {csgn}\left (\frac {i}{x -4}\right )^{3}-4 \pi \mathrm {csgn}\left (\frac {i}{x -4}\right )^{3} {\mathrm e}^{2 x}+4 \pi \mathrm {csgn}\left (\frac {i}{x -4}\right )^{2} {\mathrm e}^{2 x}-4 \ln \relax (2) \pi \mathrm {csgn}\left (\frac {i}{x -4}\right )^{2}+4 \ln \relax (2) \pi -4 \pi \,{\mathrm e}^{2 x}-4 \pi \ln \relax (2) x \mathrm {csgn}\left (\frac {i}{x -4}\right )^{2}+4 \pi x \mathrm {csgn}\left (\frac {i}{x -4}\right )^{2} {\mathrm e}^{2 x}-16 i \ln \relax (2)\right )}{4 \left (-x \,{\mathrm e}^{2 x}+x \ln \relax (2)-{\mathrm e}^{2 x}+\ln \relax (2)\right )}\right )-\ln \left (\ln \left (x -4\right )-\frac {i \left (-2 \pi \mathrm {csgn}\left (\frac {i}{x -4}\right )^{2}+2 \pi \mathrm {csgn}\left (\frac {i}{x -4}\right )^{3}-4 i \ln \relax (2)+2 \pi -8 i\right )}{2}\right )\) |
\(318\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((4*x-16)*exp(x)^4+(-8*x+32)*ln(2)*exp(x)^2+(4*x-16)*ln(2)^2)*ln(-4/(x-4))^2+((32*x-128)*exp(x)^4+((-64*x
+256)*ln(2)-2*x^2+9*x-4)*exp(x)^2+(32*x-128)*ln(2)^2+(-x+4)*ln(2))*ln(-4/(x-4))+(64*x-256)*exp(x)^4+((-128*x+5
12)*ln(2)-8*x^2+37*x-16)*exp(x)^2+(64*x-256)*ln(2)^2+(-5*x+16)*ln(2))/(((4*x^2-12*x-16)*exp(x)^4+(-8*x^2+24*x+
32)*ln(2)*exp(x)^2+(4*x^2-12*x-16)*ln(2)^2)*ln(-4/(x-4))^2+((32*x^2-96*x-128)*exp(x)^4+((-64*x^2+192*x+256)*ln
(2)+x^2-4*x)*exp(x)^2+(32*x^2-96*x-128)*ln(2)^2+(-x^2+4*x)*ln(2))*ln(-4/(x-4))+(64*x^2-192*x-256)*exp(x)^4+((-
128*x^2+384*x+512)*ln(2)+4*x^2-16*x)*exp(x)^2+(64*x^2-192*x-256)*ln(2)^2+(-4*x^2+16*x)*ln(2)),x,method=_RETURN
VERBOSE)
[Out]
ln(x+1)+ln(ln(x-4)-1/4*I*(4*Pi*ln(2)*x-4*Pi*x*exp(2*x)+16*I*x*exp(2*x)-16*I*ln(2)*x+8*I*ln(2)*x*exp(2*x)-4*Pi*
x*csgn(I/(x-4))^3*exp(2*x)+4*Pi*ln(2)*x*csgn(I/(x-4))^3+8*I*exp(2*x)*ln(2)-8*I*ln(2)^2+I*x-8*I*ln(2)^2*x+16*I*
exp(2*x)+4*ln(2)*Pi*csgn(I/(x-4))^3-4*Pi*csgn(I/(x-4))^3*exp(2*x)+4*Pi*csgn(I/(x-4))^2*exp(2*x)-4*ln(2)*Pi*csg
n(I/(x-4))^2+4*ln(2)*Pi-4*Pi*exp(2*x)-4*Pi*ln(2)*x*csgn(I/(x-4))^2+4*Pi*x*csgn(I/(x-4))^2*exp(2*x)-16*I*ln(2))
/(-x*exp(2*x)+x*ln(2)-exp(2*x)+ln(2)))-ln(ln(x-4)-1/2*I*(-2*Pi*csgn(I/(x-4))^2+2*Pi*csgn(I/(x-4))^3-4*I*ln(2)+
2*Pi-8*I))
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maxima [B] time = 0.86, size = 110, normalized size = 2.97 \begin {gather*} \log \left (x + 1\right ) + \log \left (\frac {{\left (8 \, \log \relax (2)^{2} + 16 \, \log \relax (2) - 1\right )} x - 8 \, {\left (x {\left (\log \relax (2) + 2\right )} + \log \relax (2) + 2\right )} e^{\left (2 \, x\right )} + 8 \, \log \relax (2)^{2} + 4 \, {\left ({\left (x + 1\right )} e^{\left (2 \, x\right )} - x \log \relax (2) - \log \relax (2)\right )} \log \left (-x + 4\right ) + 16 \, \log \relax (2)}{4 \, {\left ({\left (x + 1\right )} e^{\left (2 \, x\right )} - x \log \relax (2) - \log \relax (2)\right )}}\right ) - \log \left (-2 \, \log \relax (2) + \log \left (-x + 4\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x-16)*exp(x)^4+(-8*x+32)*log(2)*exp(x)^2+(4*x-16)*log(2)^2)*log(-4/(x-4))^2+((32*x-128)*exp(x)^
4+((-64*x+256)*log(2)-2*x^2+9*x-4)*exp(x)^2+(32*x-128)*log(2)^2+(-x+4)*log(2))*log(-4/(x-4))+(64*x-256)*exp(x)
^4+((-128*x+512)*log(2)-8*x^2+37*x-16)*exp(x)^2+(64*x-256)*log(2)^2+(-5*x+16)*log(2))/(((4*x^2-12*x-16)*exp(x)
^4+(-8*x^2+24*x+32)*log(2)*exp(x)^2+(4*x^2-12*x-16)*log(2)^2)*log(-4/(x-4))^2+((32*x^2-96*x-128)*exp(x)^4+((-6
4*x^2+192*x+256)*log(2)+x^2-4*x)*exp(x)^2+(32*x^2-96*x-128)*log(2)^2+(-x^2+4*x)*log(2))*log(-4/(x-4))+(64*x^2-
192*x-256)*exp(x)^4+((-128*x^2+384*x+512)*log(2)+4*x^2-16*x)*exp(x)^2+(64*x^2-192*x-256)*log(2)^2+(-4*x^2+16*x
)*log(2)),x, algorithm="maxima")
[Out]
log(x + 1) + log(1/4*((8*log(2)^2 + 16*log(2) - 1)*x - 8*(x*(log(2) + 2) + log(2) + 2)*e^(2*x) + 8*log(2)^2 +
4*((x + 1)*e^(2*x) - x*log(2) - log(2))*log(-x + 4) + 16*log(2))/((x + 1)*e^(2*x) - x*log(2) - log(2))) - log(
-2*log(2) + log(-x + 4) - 4)
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\left ({\mathrm {e}}^{2\,x}\,\ln \relax (2)\,\left (8\,x-32\right )-{\mathrm {e}}^{4\,x}\,\left (4\,x-16\right )-{\ln \relax (2)}^2\,\left (4\,x-16\right )\right )\,{\ln \left (-\frac {4}{x-4}\right )}^2+\left ({\mathrm {e}}^{2\,x}\,\left (\ln \relax (2)\,\left (64\,x-256\right )-9\,x+2\,x^2+4\right )-{\ln \relax (2)}^2\,\left (32\,x-128\right )+\ln \relax (2)\,\left (x-4\right )-{\mathrm {e}}^{4\,x}\,\left (32\,x-128\right )\right )\,\ln \left (-\frac {4}{x-4}\right )+\ln \relax (2)\,\left (5\,x-16\right )+{\mathrm {e}}^{2\,x}\,\left (\ln \relax (2)\,\left (128\,x-512\right )-37\,x+8\,x^2+16\right )-{\ln \relax (2)}^2\,\left (64\,x-256\right )-{\mathrm {e}}^{4\,x}\,\left (64\,x-256\right )}{\left ({\mathrm {e}}^{4\,x}\,\left (-4\,x^2+12\,x+16\right )+{\ln \relax (2)}^2\,\left (-4\,x^2+12\,x+16\right )-{\mathrm {e}}^{2\,x}\,\ln \relax (2)\,\left (-8\,x^2+24\,x+32\right )\right )\,{\ln \left (-\frac {4}{x-4}\right )}^2+\left ({\mathrm {e}}^{4\,x}\,\left (-32\,x^2+96\,x+128\right )-\ln \relax (2)\,\left (4\,x-x^2\right )+{\ln \relax (2)}^2\,\left (-32\,x^2+96\,x+128\right )-{\mathrm {e}}^{2\,x}\,\left (\ln \relax (2)\,\left (-64\,x^2+192\,x+256\right )-4\,x+x^2\right )\right )\,\ln \left (-\frac {4}{x-4}\right )+{\mathrm {e}}^{4\,x}\,\left (-64\,x^2+192\,x+256\right )-\ln \relax (2)\,\left (16\,x-4\,x^2\right )-{\mathrm {e}}^{2\,x}\,\left (\ln \relax (2)\,\left (-128\,x^2+384\,x+512\right )-16\,x+4\,x^2\right )+{\ln \relax (2)}^2\,\left (-64\,x^2+192\,x+256\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((log(2)*(5*x - 16) + exp(2*x)*(log(2)*(128*x - 512) - 37*x + 8*x^2 + 16) - log(2)^2*(64*x - 256) - log(-4/
(x - 4))^2*(log(2)^2*(4*x - 16) + exp(4*x)*(4*x - 16) - exp(2*x)*log(2)*(8*x - 32)) + log(-4/(x - 4))*(exp(2*x
)*(log(2)*(64*x - 256) - 9*x + 2*x^2 + 4) - log(2)^2*(32*x - 128) + log(2)*(x - 4) - exp(4*x)*(32*x - 128)) -
exp(4*x)*(64*x - 256))/(exp(4*x)*(192*x - 64*x^2 + 256) - log(2)*(16*x - 4*x^2) + log(-4/(x - 4))^2*(exp(4*x)*
(12*x - 4*x^2 + 16) + log(2)^2*(12*x - 4*x^2 + 16) - exp(2*x)*log(2)*(24*x - 8*x^2 + 32)) - exp(2*x)*(log(2)*(
384*x - 128*x^2 + 512) - 16*x + 4*x^2) + log(-4/(x - 4))*(exp(4*x)*(96*x - 32*x^2 + 128) - log(2)*(4*x - x^2)
+ log(2)^2*(96*x - 32*x^2 + 128) - exp(2*x)*(log(2)*(192*x - 64*x^2 + 256) - 4*x + x^2)) + log(2)^2*(192*x - 6
4*x^2 + 256)),x)
[Out]
int((log(2)*(5*x - 16) + exp(2*x)*(log(2)*(128*x - 512) - 37*x + 8*x^2 + 16) - log(2)^2*(64*x - 256) - log(-4/
(x - 4))^2*(log(2)^2*(4*x - 16) + exp(4*x)*(4*x - 16) - exp(2*x)*log(2)*(8*x - 32)) + log(-4/(x - 4))*(exp(2*x
)*(log(2)*(64*x - 256) - 9*x + 2*x^2 + 4) - log(2)^2*(32*x - 128) + log(2)*(x - 4) - exp(4*x)*(32*x - 128)) -
exp(4*x)*(64*x - 256))/(exp(4*x)*(192*x - 64*x^2 + 256) - log(2)*(16*x - 4*x^2) + log(-4/(x - 4))^2*(exp(4*x)*
(12*x - 4*x^2 + 16) + log(2)^2*(12*x - 4*x^2 + 16) - exp(2*x)*log(2)*(24*x - 8*x^2 + 32)) - exp(2*x)*(log(2)*(
384*x - 128*x^2 + 512) - 16*x + 4*x^2) + log(-4/(x - 4))*(exp(4*x)*(96*x - 32*x^2 + 128) - log(2)*(4*x - x^2)
+ log(2)^2*(96*x - 32*x^2 + 128) - exp(2*x)*(log(2)*(192*x - 64*x^2 + 256) - 4*x + x^2)) + log(2)^2*(192*x - 6
4*x^2 + 256)), x)
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sympy [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: PolynomialError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x-16)*exp(x)**4+(-8*x+32)*ln(2)*exp(x)**2+(4*x-16)*ln(2)**2)*ln(-4/(x-4))**2+((32*x-128)*exp(x)
**4+((-64*x+256)*ln(2)-2*x**2+9*x-4)*exp(x)**2+(32*x-128)*ln(2)**2+(-x+4)*ln(2))*ln(-4/(x-4))+(64*x-256)*exp(x
)**4+((-128*x+512)*ln(2)-8*x**2+37*x-16)*exp(x)**2+(64*x-256)*ln(2)**2+(-5*x+16)*ln(2))/(((4*x**2-12*x-16)*exp
(x)**4+(-8*x**2+24*x+32)*ln(2)*exp(x)**2+(4*x**2-12*x-16)*ln(2)**2)*ln(-4/(x-4))**2+((32*x**2-96*x-128)*exp(x)
**4+((-64*x**2+192*x+256)*ln(2)+x**2-4*x)*exp(x)**2+(32*x**2-96*x-128)*ln(2)**2+(-x**2+4*x)*ln(2))*ln(-4/(x-4)
)+(64*x**2-192*x-256)*exp(x)**4+((-128*x**2+384*x+512)*ln(2)+4*x**2-16*x)*exp(x)**2+(64*x**2-192*x-256)*ln(2)*
*2+(-4*x**2+16*x)*ln(2)),x)
[Out]
Exception raised: PolynomialError
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