3.82.22 \(\int \frac {256 x^3-12288 x^4+e^{4 e^x+4 x} (-48 x^4+64 x^5+64 e^x x^5)+e^{3 e^x+3 x} (-768 x^4+768 x^5+768 e^x x^5)+e^{2 e^x+2 x} (-4608 x^4+3072 x^5+3072 e^x x^5)+e^{e^x+x} (-12288 x^4+4096 x^5+4096 e^x x^5)}{16-2048 x+65536 x^2+3584 e^{5 e^x+5 x} x^2+448 e^{6 e^x+6 x} x^2+32 e^{7 e^x+7 x} x^2+e^{8 e^x+8 x} x^2+e^{4 e^x+4 x} (-8 x+17920 x^2)+e^{3 e^x+3 x} (-128 x+57344 x^2)+e^{2 e^x+2 x} (-768 x+114688 x^2)+e^{e^x+x} (-2048 x+131072 x^2)} \, dx\)
Optimal. Leaf size=23 \[ \frac {16 x^4}{4-\left (4+e^{e^x+x}\right )^4 x} \]
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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[(256*x^3 - 12288*x^4 + E^(4*E^x + 4*x)*(-48*x^4 + 64*x^5 + 64*E^x*x^5) + E^(3*E^x + 3*x)*(-768*x^4 + 768*x
^5 + 768*E^x*x^5) + E^(2*E^x + 2*x)*(-4608*x^4 + 3072*x^5 + 3072*E^x*x^5) + E^(E^x + x)*(-12288*x^4 + 4096*x^5
+ 4096*E^x*x^5))/(16 - 2048*x + 65536*x^2 + 3584*E^(5*E^x + 5*x)*x^2 + 448*E^(6*E^x + 6*x)*x^2 + 32*E^(7*E^x
+ 7*x)*x^2 + E^(8*E^x + 8*x)*x^2 + E^(4*E^x + 4*x)*(-8*x + 17920*x^2) + E^(3*E^x + 3*x)*(-128*x + 57344*x^2) +
E^(2*E^x + 2*x)*(-768*x + 114688*x^2) + E^(E^x + x)*(-2048*x + 131072*x^2)),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [A] time = 2.48, size = 22, normalized size = 0.96 \begin {gather*} -\frac {16 x^4}{-4+\left (4+e^{e^x+x}\right )^4 x} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(256*x^3 - 12288*x^4 + E^(4*E^x + 4*x)*(-48*x^4 + 64*x^5 + 64*E^x*x^5) + E^(3*E^x + 3*x)*(-768*x^4 +
768*x^5 + 768*E^x*x^5) + E^(2*E^x + 2*x)*(-4608*x^4 + 3072*x^5 + 3072*E^x*x^5) + E^(E^x + x)*(-12288*x^4 + 40
96*x^5 + 4096*E^x*x^5))/(16 - 2048*x + 65536*x^2 + 3584*E^(5*E^x + 5*x)*x^2 + 448*E^(6*E^x + 6*x)*x^2 + 32*E^(
7*E^x + 7*x)*x^2 + E^(8*E^x + 8*x)*x^2 + E^(4*E^x + 4*x)*(-8*x + 17920*x^2) + E^(3*E^x + 3*x)*(-128*x + 57344*
x^2) + E^(2*E^x + 2*x)*(-768*x + 114688*x^2) + E^(E^x + x)*(-2048*x + 131072*x^2)),x]
[Out]
(-16*x^4)/(-4 + (4 + E^(E^x + x))^4*x)
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fricas [B] time = 1.52, size = 55, normalized size = 2.39 \begin {gather*} -\frac {16 \, x^{4}}{x e^{\left (4 \, x + 4 \, e^{x}\right )} + 16 \, x e^{\left (3 \, x + 3 \, e^{x}\right )} + 96 \, x e^{\left (2 \, x + 2 \, e^{x}\right )} + 256 \, x e^{\left (x + e^{x}\right )} + 256 \, x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((64*x^5*exp(x)+64*x^5-48*x^4)*exp(exp(x)+x)^4+(768*x^5*exp(x)+768*x^5-768*x^4)*exp(exp(x)+x)^3+(307
2*x^5*exp(x)+3072*x^5-4608*x^4)*exp(exp(x)+x)^2+(4096*x^5*exp(x)+4096*x^5-12288*x^4)*exp(exp(x)+x)-12288*x^4+2
56*x^3)/(x^2*exp(exp(x)+x)^8+32*x^2*exp(exp(x)+x)^7+448*x^2*exp(exp(x)+x)^6+3584*x^2*exp(exp(x)+x)^5+(17920*x^
2-8*x)*exp(exp(x)+x)^4+(57344*x^2-128*x)*exp(exp(x)+x)^3+(114688*x^2-768*x)*exp(exp(x)+x)^2+(131072*x^2-2048*x
)*exp(exp(x)+x)+65536*x^2-2048*x+16),x, algorithm="fricas")
[Out]
-16*x^4/(x*e^(4*x + 4*e^x) + 16*x*e^(3*x + 3*e^x) + 96*x*e^(2*x + 2*e^x) + 256*x*e^(x + e^x) + 256*x - 4)
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((64*x^5*exp(x)+64*x^5-48*x^4)*exp(exp(x)+x)^4+(768*x^5*exp(x)+768*x^5-768*x^4)*exp(exp(x)+x)^3+(307
2*x^5*exp(x)+3072*x^5-4608*x^4)*exp(exp(x)+x)^2+(4096*x^5*exp(x)+4096*x^5-12288*x^4)*exp(exp(x)+x)-12288*x^4+2
56*x^3)/(x^2*exp(exp(x)+x)^8+32*x^2*exp(exp(x)+x)^7+448*x^2*exp(exp(x)+x)^6+3584*x^2*exp(exp(x)+x)^5+(17920*x^
2-8*x)*exp(exp(x)+x)^4+(57344*x^2-128*x)*exp(exp(x)+x)^3+(114688*x^2-768*x)*exp(exp(x)+x)^2+(131072*x^2-2048*x
)*exp(exp(x)+x)+65536*x^2-2048*x+16),x, algorithm="giac")
[Out]
Timed out
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maple [B] time = 0.10, size = 56, normalized size = 2.43
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result |
size |
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| risch |
\(-\frac {16 x^{4}}{{\mathrm e}^{4 \,{\mathrm e}^{x}+4 x} x +16 \,{\mathrm e}^{3 \,{\mathrm e}^{x}+3 x} x +96 \,{\mathrm e}^{2 \,{\mathrm e}^{x}+2 x} x +256 \,{\mathrm e}^{{\mathrm e}^{x}+x} x +256 x -4}\) |
\(56\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((64*x^5*exp(x)+64*x^5-48*x^4)*exp(exp(x)+x)^4+(768*x^5*exp(x)+768*x^5-768*x^4)*exp(exp(x)+x)^3+(3072*x^5*
exp(x)+3072*x^5-4608*x^4)*exp(exp(x)+x)^2+(4096*x^5*exp(x)+4096*x^5-12288*x^4)*exp(exp(x)+x)-12288*x^4+256*x^3
)/(x^2*exp(exp(x)+x)^8+32*x^2*exp(exp(x)+x)^7+448*x^2*exp(exp(x)+x)^6+3584*x^2*exp(exp(x)+x)^5+(17920*x^2-8*x)
*exp(exp(x)+x)^4+(57344*x^2-128*x)*exp(exp(x)+x)^3+(114688*x^2-768*x)*exp(exp(x)+x)^2+(131072*x^2-2048*x)*exp(
exp(x)+x)+65536*x^2-2048*x+16),x,method=_RETURNVERBOSE)
[Out]
-16*x^4/(exp(4*exp(x)+4*x)*x+16*exp(3*exp(x)+3*x)*x+96*exp(2*exp(x)+2*x)*x+256*exp(exp(x)+x)*x+256*x-4)
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maxima [B] time = 0.56, size = 55, normalized size = 2.39 \begin {gather*} -\frac {16 \, x^{4}}{x e^{\left (4 \, x + 4 \, e^{x}\right )} + 16 \, x e^{\left (3 \, x + 3 \, e^{x}\right )} + 96 \, x e^{\left (2 \, x + 2 \, e^{x}\right )} + 256 \, x e^{\left (x + e^{x}\right )} + 256 \, x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((64*x^5*exp(x)+64*x^5-48*x^4)*exp(exp(x)+x)^4+(768*x^5*exp(x)+768*x^5-768*x^4)*exp(exp(x)+x)^3+(307
2*x^5*exp(x)+3072*x^5-4608*x^4)*exp(exp(x)+x)^2+(4096*x^5*exp(x)+4096*x^5-12288*x^4)*exp(exp(x)+x)-12288*x^4+2
56*x^3)/(x^2*exp(exp(x)+x)^8+32*x^2*exp(exp(x)+x)^7+448*x^2*exp(exp(x)+x)^6+3584*x^2*exp(exp(x)+x)^5+(17920*x^
2-8*x)*exp(exp(x)+x)^4+(57344*x^2-128*x)*exp(exp(x)+x)^3+(114688*x^2-768*x)*exp(exp(x)+x)^2+(131072*x^2-2048*x
)*exp(exp(x)+x)+65536*x^2-2048*x+16),x, algorithm="maxima")
[Out]
-16*x^4/(x*e^(4*x + 4*e^x) + 16*x*e^(3*x + 3*e^x) + 96*x*e^(2*x + 2*e^x) + 256*x*e^(x + e^x) + 256*x - 4)
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{4\,x+4\,{\mathrm {e}}^x}\,\left (64\,x^5\,{\mathrm {e}}^x-48\,x^4+64\,x^5\right )+{\mathrm {e}}^{3\,x+3\,{\mathrm {e}}^x}\,\left (768\,x^5\,{\mathrm {e}}^x-768\,x^4+768\,x^5\right )+{\mathrm {e}}^{2\,x+2\,{\mathrm {e}}^x}\,\left (3072\,x^5\,{\mathrm {e}}^x-4608\,x^4+3072\,x^5\right )+{\mathrm {e}}^{x+{\mathrm {e}}^x}\,\left (4096\,x^5\,{\mathrm {e}}^x-12288\,x^4+4096\,x^5\right )+256\,x^3-12288\,x^4}{3584\,x^2\,{\mathrm {e}}^{5\,x+5\,{\mathrm {e}}^x}-2048\,x+448\,x^2\,{\mathrm {e}}^{6\,x+6\,{\mathrm {e}}^x}+32\,x^2\,{\mathrm {e}}^{7\,x+7\,{\mathrm {e}}^x}+x^2\,{\mathrm {e}}^{8\,x+8\,{\mathrm {e}}^x}-{\mathrm {e}}^{4\,x+4\,{\mathrm {e}}^x}\,\left (8\,x-17920\,x^2\right )-{\mathrm {e}}^{3\,x+3\,{\mathrm {e}}^x}\,\left (128\,x-57344\,x^2\right )-{\mathrm {e}}^{2\,x+2\,{\mathrm {e}}^x}\,\left (768\,x-114688\,x^2\right )+65536\,x^2-{\mathrm {e}}^{x+{\mathrm {e}}^x}\,\left (2048\,x-131072\,x^2\right )+16} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp(4*x + 4*exp(x))*(64*x^5*exp(x) - 48*x^4 + 64*x^5) + exp(3*x + 3*exp(x))*(768*x^5*exp(x) - 768*x^4 + 7
68*x^5) + exp(2*x + 2*exp(x))*(3072*x^5*exp(x) - 4608*x^4 + 3072*x^5) + exp(x + exp(x))*(4096*x^5*exp(x) - 122
88*x^4 + 4096*x^5) + 256*x^3 - 12288*x^4)/(3584*x^2*exp(5*x + 5*exp(x)) - 2048*x + 448*x^2*exp(6*x + 6*exp(x))
+ 32*x^2*exp(7*x + 7*exp(x)) + x^2*exp(8*x + 8*exp(x)) - exp(4*x + 4*exp(x))*(8*x - 17920*x^2) - exp(3*x + 3*
exp(x))*(128*x - 57344*x^2) - exp(2*x + 2*exp(x))*(768*x - 114688*x^2) + 65536*x^2 - exp(x + exp(x))*(2048*x -
131072*x^2) + 16),x)
[Out]
int((exp(4*x + 4*exp(x))*(64*x^5*exp(x) - 48*x^4 + 64*x^5) + exp(3*x + 3*exp(x))*(768*x^5*exp(x) - 768*x^4 + 7
68*x^5) + exp(2*x + 2*exp(x))*(3072*x^5*exp(x) - 4608*x^4 + 3072*x^5) + exp(x + exp(x))*(4096*x^5*exp(x) - 122
88*x^4 + 4096*x^5) + 256*x^3 - 12288*x^4)/(3584*x^2*exp(5*x + 5*exp(x)) - 2048*x + 448*x^2*exp(6*x + 6*exp(x))
+ 32*x^2*exp(7*x + 7*exp(x)) + x^2*exp(8*x + 8*exp(x)) - exp(4*x + 4*exp(x))*(8*x - 17920*x^2) - exp(3*x + 3*
exp(x))*(128*x - 57344*x^2) - exp(2*x + 2*exp(x))*(768*x - 114688*x^2) + 65536*x^2 - exp(x + exp(x))*(2048*x -
131072*x^2) + 16), x)
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sympy [B] time = 0.50, size = 60, normalized size = 2.61 \begin {gather*} - \frac {16 x^{4}}{256 x e^{x + e^{x}} + 96 x e^{2 x + 2 e^{x}} + 16 x e^{3 x + 3 e^{x}} + x e^{4 x + 4 e^{x}} + 256 x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((64*x**5*exp(x)+64*x**5-48*x**4)*exp(exp(x)+x)**4+(768*x**5*exp(x)+768*x**5-768*x**4)*exp(exp(x)+x)
**3+(3072*x**5*exp(x)+3072*x**5-4608*x**4)*exp(exp(x)+x)**2+(4096*x**5*exp(x)+4096*x**5-12288*x**4)*exp(exp(x)
+x)-12288*x**4+256*x**3)/(x**2*exp(exp(x)+x)**8+32*x**2*exp(exp(x)+x)**7+448*x**2*exp(exp(x)+x)**6+3584*x**2*e
xp(exp(x)+x)**5+(17920*x**2-8*x)*exp(exp(x)+x)**4+(57344*x**2-128*x)*exp(exp(x)+x)**3+(114688*x**2-768*x)*exp(
exp(x)+x)**2+(131072*x**2-2048*x)*exp(exp(x)+x)+65536*x**2-2048*x+16),x)
[Out]
-16*x**4/(256*x*exp(x + exp(x)) + 96*x*exp(2*x + 2*exp(x)) + 16*x*exp(3*x + 3*exp(x)) + x*exp(4*x + 4*exp(x))
+ 256*x - 4)
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