3.63.8 \(\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} (400+50 x+25 x^2)}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5)+e^{\frac {2 (8+2 x)}{x^2}} (-24 e^2 x^3+192 e x^4-384 x^5)+e^{\frac {8+2 x}{x^2}} (24 e x^4-96 x^5)} \, dx\) [6208]
Optimal. Leaf size=30 \[ \frac {1}{16 \left (-x+\frac {1}{5} \left (e+x-e^{-\frac {2 (4+x)}{x^2}} x\right )\right )^2} \]
[Out]
1/4/(1/5*exp(1)-4/5*x-1/5*x/exp(2*(4+x)/x^2))/(4/5*exp(1)-16/5*x-4/5*x/exp(2*(4+x)/x^2))
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Rubi [F]
time = 4.86, 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 {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(100*E^((3*(8 + 2*x))/x^2)*x^2 + E^((2*(8 + 2*x))/x^2)*(400 + 50*x + 25*x^2))/(-8*x^5 + E^((3*(8 + 2*x))/x
^2)*(8*E^3*x^2 - 96*E^2*x^3 + 384*E*x^4 - 512*x^5) + E^((2*(8 + 2*x))/x^2)*(-24*E^2*x^3 + 192*E*x^4 - 384*x^5)
+ E^((8 + 2*x)/x^2)*(24*E*x^4 - 96*x^5)),x]
[Out]
(25*Defer[Int][E^(1 + (4*(4 + x))/x^2)/((E - 4*x)*(E^(1 + 8/x^2 + 2/x) - x - 4*E^(8/x^2 + 2/x)*x)^3), x])/8 +
(25*Defer[Int][E^((4*(4 + x))/x^2)/((E - 4*x)*(E^(1 + 8/x^2 + 2/x) - x - 4*E^(8/x^2 + 2/x)*x)^2), x])/2 - 50*D
efer[Int][E^((4*(4 + x))/x^2)/(x^2*(-E^(1 + 8/x^2 + 2/x) + x + 4*E^(8/x^2 + 2/x)*x)^3), x] - (25*Defer[Int][E^
((4*(4 + x))/x^2)/(x*(-E^(1 + 8/x^2 + 2/x) + x + 4*E^(8/x^2 + 2/x)*x)^3), x])/4
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {25 e^{\frac {4 (4+x)}{x^2}} \left (16+2 x+\left (1+4 e^{\frac {2 (4+x)}{x^2}}\right ) x^2\right )}{8 x^2 \left (e^{\frac {8+2 x+x^2}{x^2}}-x-4 e^{\frac {2 (4+x)}{x^2}} x\right )^3} \, dx\\ &=\frac {25}{8} \int \frac {e^{\frac {4 (4+x)}{x^2}} \left (16+2 x+\left (1+4 e^{\frac {2 (4+x)}{x^2}}\right ) x^2\right )}{x^2 \left (e^{\frac {8+2 x+x^2}{x^2}}-x-4 e^{\frac {2 (4+x)}{x^2}} x\right )^3} \, dx\\ &=\frac {25}{8} \int \left (\frac {4 e^{\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^2}+\frac {e^{\frac {4 (4+x)}{x^2}} \left (16 e-2 (32-e) x-(8-e) x^2\right )}{(e-4 x) x^2 \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3}\right ) \, dx\\ &=\frac {25}{8} \int \frac {e^{\frac {4 (4+x)}{x^2}} \left (16 e-2 (32-e) x-(8-e) x^2\right )}{(e-4 x) x^2 \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3} \, dx+\frac {25}{2} \int \frac {e^{\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^2} \, dx\\ &=\frac {25}{8} \int \left (\frac {e^{1+\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3}-\frac {16 e^{\frac {4 (4+x)}{x^2}}}{x^2 \left (-e^{1+\frac {8}{x^2}+\frac {2}{x}}+x+4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3}-\frac {2 e^{\frac {4 (4+x)}{x^2}}}{x \left (-e^{1+\frac {8}{x^2}+\frac {2}{x}}+x+4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3}\right ) \, dx+\frac {25}{2} \int \frac {e^{\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^2} \, dx\\ &=\frac {25}{8} \int \frac {e^{1+\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3} \, dx-\frac {25}{4} \int \frac {e^{\frac {4 (4+x)}{x^2}}}{x \left (-e^{1+\frac {8}{x^2}+\frac {2}{x}}+x+4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3} \, dx+\frac {25}{2} \int \frac {e^{\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^2} \, dx-50 \int \frac {e^{\frac {4 (4+x)}{x^2}}}{x^2 \left (-e^{1+\frac {8}{x^2}+\frac {2}{x}}+x+4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.42, size = 47, normalized size = 1.57 \begin {gather*} \frac {25 e^{\frac {4 (4+x)}{x^2}}}{16 \left (-e^{\frac {8+2 x+x^2}{x^2}}+x+4 e^{\frac {2 (4+x)}{x^2}} x\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(100*E^((3*(8 + 2*x))/x^2)*x^2 + E^((2*(8 + 2*x))/x^2)*(400 + 50*x + 25*x^2))/(-8*x^5 + E^((3*(8 + 2
*x))/x^2)*(8*E^3*x^2 - 96*E^2*x^3 + 384*E*x^4 - 512*x^5) + E^((2*(8 + 2*x))/x^2)*(-24*E^2*x^3 + 192*E*x^4 - 38
4*x^5) + E^((8 + 2*x)/x^2)*(24*E*x^4 - 96*x^5)),x]
[Out]
(25*E^((4*(4 + x))/x^2))/(16*(-E^((8 + 2*x + x^2)/x^2) + x + 4*E^((2*(4 + x))/x^2)*x)^2)
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Maple [A]
time = 1.38, size = 47, normalized size = 1.57
| | |
| method |
result |
size |
| | |
| norman |
\(\frac {25 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}}}{16 \left ({\mathrm e} \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-4 x \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-x \right )^{2}}\) |
\(47\) |
| risch |
\(\frac {25}{16 \left ({\mathrm e}^{2}-8 x \,{\mathrm e}+16 x^{2}\right )}+\frac {25 \left (2 \,{\mathrm e}^{\frac {x^{2}+2 x +8}{x^{2}}}-8 x \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-x \right ) x}{16 \left ({\mathrm e}^{2}-8 x \,{\mathrm e}+16 x^{2}\right ) \left ({\mathrm e}^{\frac {x^{2}+2 x +8}{x^{2}}}-4 x \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-x \right )^{2}}\) |
\(99\) |
| | |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+384*x^4
*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4*exp(1
)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x,method=_RETURNVERBOSE)
[Out]
25/16*exp((2*x+8)/x^2)^2/(exp(1)*exp((2*x+8)/x^2)-4*x*exp((2*x+8)/x^2)-x)^2
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 71 vs.
\(2 (23) = 46\).
time = 0.45, size = 71, normalized size = 2.37 \begin {gather*} \frac {25 \, e^{\left (\frac {4}{x} + \frac {16}{x^{2}}\right )}}{16 \, {\left (x^{2} + {\left (16 \, x^{2} - 8 \, x e + e^{2}\right )} e^{\left (\frac {4}{x} + \frac {16}{x^{2}}\right )} + 2 \, {\left (4 \, x^{2} - x e\right )} e^{\left (\frac {2}{x} + \frac {8}{x^{2}}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+3
84*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4
*exp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="maxima")
[Out]
25/16*e^(4/x + 16/x^2)/(x^2 + (16*x^2 - 8*x*e + e^2)*e^(4/x + 16/x^2) + 2*(4*x^2 - x*e)*e^(2/x + 8/x^2))
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 62 vs.
\(2 (23) = 46\).
time = 0.42, size = 62, normalized size = 2.07 \begin {gather*} \frac {25 \, e^{\left (\frac {4 \, {\left (x + 4\right )}}{x^{2}}\right )}}{16 \, {\left (x^{2} + {\left (16 \, x^{2} - 8 \, x e + e^{2}\right )} e^{\left (\frac {4 \, {\left (x + 4\right )}}{x^{2}}\right )} + 2 \, {\left (4 \, x^{2} - x e\right )} e^{\left (\frac {2 \, {\left (x + 4\right )}}{x^{2}}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+3
84*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4
*exp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="fricas")
[Out]
25/16*e^(4*(x + 4)/x^2)/(x^2 + (16*x^2 - 8*x*e + e^2)*e^(4*(x + 4)/x^2) + 2*(4*x^2 - x*e)*e^(2*(x + 4)/x^2))
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 150 vs.
\(2 (53) = 106\).
time = 0.30, size = 150, normalized size = 5.00 \begin {gather*} \frac {- 25 x^{2} + \left (- 200 x^{2} + 50 e x\right ) e^{\frac {2 x + 8}{x^{2}}}}{256 x^{4} - 128 e x^{3} + 16 x^{2} e^{2} + \left (2048 x^{4} - 1536 e x^{3} + 384 x^{2} e^{2} - 32 x e^{3}\right ) e^{\frac {2 x + 8}{x^{2}}} + \left (4096 x^{4} - 4096 e x^{3} + 1536 x^{2} e^{2} - 256 x e^{3} + 16 e^{4}\right ) e^{\frac {2 \cdot \left (2 x + 8\right )}{x^{2}}}} + \frac {25}{256 x^{2} - 128 e x + 16 e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((100*x**2*exp((2*x+8)/x**2)**3+(25*x**2+50*x+400)*exp((2*x+8)/x**2)**2)/((8*x**2*exp(1)**3-96*x**3*e
xp(1)**2+384*x**4*exp(1)-512*x**5)*exp((2*x+8)/x**2)**3+(-24*x**3*exp(1)**2+192*x**4*exp(1)-384*x**5)*exp((2*x
+8)/x**2)**2+(24*x**4*exp(1)-96*x**5)*exp((2*x+8)/x**2)-8*x**5),x)
[Out]
(-25*x**2 + (-200*x**2 + 50*E*x)*exp((2*x + 8)/x**2))/(256*x**4 - 128*E*x**3 + 16*x**2*exp(2) + (2048*x**4 - 1
536*E*x**3 + 384*x**2*exp(2) - 32*x*exp(3))*exp((2*x + 8)/x**2) + (4096*x**4 - 4096*E*x**3 + 1536*x**2*exp(2)
- 256*x*exp(3) + 16*exp(4))*exp(2*(2*x + 8)/x**2)) + 25/(256*x**2 - 128*E*x + 16*exp(2))
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 28878 vs.
\(2 (23) = 46\).
time = 0.73, size = 28878, normalized size = 962.60 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+3
84*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4
*exp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="giac")
[Out]
25/16*(65536*x^14*e^(22*(x + 4)/x^2) + 131072*x^14*e^(20*(x + 4)/x^2) + 114688*x^14*e^(18*(x + 4)/x^2) + 57344
*x^14*e^(16*(x + 4)/x^2) + 17920*x^14*e^(14*(x + 4)/x^2) + 3584*x^14*e^(12*(x + 4)/x^2) + 448*x^14*e^(10*(x +
4)/x^2) + 32*x^14*e^(8*(x + 4)/x^2) + x^14*e^(6*(x + 4)/x^2) - 8192*x^13*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/
x^2) - 12288*x^13*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 7680*x^13*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x
^2) - 2560*x^13*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 480*x^13*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2)
- 48*x^13*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 2*x^13*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 32768*x
^13*e^((x^2 + 2*x + 8)/x^2 + 20*(x + 4)/x^2) - 49152*x^13*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 30720*x^1
3*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 10240*x^13*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 1920*x^13*e
^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 192*x^13*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 8*x^13*e^((x^2 +
2*x + 8)/x^2 + 8*(x + 4)/x^2) + 196608*x^13*e^(20*(x + 4)/x^2) + 344064*x^13*e^(18*(x + 4)/x^2) + 258048*x^13
*e^(16*(x + 4)/x^2) + 107520*x^13*e^(14*(x + 4)/x^2) + 26880*x^13*e^(12*(x + 4)/x^2) + 4032*x^13*e^(10*(x + 4)
/x^2) + 336*x^13*e^(8*(x + 4)/x^2) + 12*x^13*e^(6*(x + 4)/x^2) + 1024*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x +
4)/x^2) + 1280*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 640*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x
+ 4)/x^2) + 160*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 20*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4
)/x^2) + x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) - 16384*x^12*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2
) - 45056*x^12*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 40960*x^12*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2
) - 17920*x^12*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 4160*x^12*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2)
- 496*x^12*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 24*x^12*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) + 4096*
x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) + 5120*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) + 2560*
x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) + 640*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 80*x^1
2*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 4*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 81920*x^12*e
^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 102400*x^12*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 51200*x^12*e^
((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 12800*x^12*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 1600*x^12*e^((x
^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 80*x^12*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 1572864*x^12*e^(20*(x
+ 4)/x^2) + 2998272*x^12*e^(18*(x + 4)/x^2) + 2433024*x^12*e^(16*(x + 4)/x^2) + 1090560*x^12*e^(14*(x + 4)/x^2
) + 291840*x^12*e^(12*(x + 4)/x^2) + 46656*x^12*e^(10*(x + 4)/x^2) + 4128*x^12*e^(8*(x + 4)/x^2) + 156*x^12*e^
(6*(x + 4)/x^2) + 2048*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 5120*x^11*e^(2*(x^2 + 3*x + 12)/x^2
+ 12*(x + 4)/x^2) + 3840*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 1280*x^11*e^(2*(x^2 + 3*x + 12)/x^
2 + 8*(x + 4)/x^2) + 200*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 12*x^11*e^(2*(x^2 + 3*x + 12)/x^2 +
4*(x + 4)/x^2) - 81920*x^11*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 339968*x^11*e^((x^2 + 3*x + 12)/x^2 +
15*(x + 4)/x^2) - 368640*x^11*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 181760*x^11*e^((x^2 + 3*x + 12)/x^2
+ 11*(x + 4)/x^2) - 46400*x^11*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 6000*x^11*e^((x^2 + 3*x + 12)/x^2 +
7*(x + 4)/x^2) - 312*x^11*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) + 10240*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 16
*(x + 4)/x^2) + 10240*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) + 3840*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 1
2*(x + 4)/x^2) + 640*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 40*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x
+ 4)/x^2) - 704512*x^11*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 962560*x^11*e^((x^2 + 2*x + 8)/x^2 + 16*(x
+ 4)/x^2) - 522240*x^11*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 140800*x^11*e^((x^2 + 2*x + 8)/x^2 + 12*(x
+ 4)/x^2) - 18880*x^11*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 1008*x^11*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4
)/x^2) + 3932160*x^11*e^(18*(x + 4)/x^2) + 6062080*x^11*e^(16*(x + 4)/x^2) + 3891200*x^11*e^(14*(x + 4)/x^2) +
1331200*x^11*e^(12*(x + 4)/x^2) + 256000*x^11*e^(10*(x + 4)/x^2) + 26240*x^11*e^(8*(x + 4)/x^2) + 1120*x^11*e
^(6*(x + 4)/x^2) + 4096*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 33792*x^10*e^(2*(x^2 + 3*x + 12)/x^
2 + 12*(x + 4)/x^2) + 33792*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 13312*x^10*e^(2*(x^2 + 3*x + 12
)/x^2 + 8*(x + 4)/x^2) + 2352*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 156*x^10*e^(2*(x^2 + 3*x + 12)
/x^2 + 4*(x + 4)/x^2) - 262144*x^10*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 909312*x^10*e^((x^2 + 3*x + 12
)/x^2 + 15*(x + 4)/x^2) - 1277952*x^10*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 801792*x^10*e^((x^2 + 3*x +
12)/x^2 + 11*(x + 4)/x^2) - 248832*x^10*e^((x^...
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {100\,x^2\,{\mathrm {e}}^{\frac {3\,\left (2\,x+8\right )}{x^2}}+{\mathrm {e}}^{\frac {2\,\left (2\,x+8\right )}{x^2}}\,\left (25\,x^2+50\,x+400\right )}{{\mathrm {e}}^{\frac {2\,\left (2\,x+8\right )}{x^2}}\,\left (384\,x^5-192\,\mathrm {e}\,x^4+24\,{\mathrm {e}}^2\,x^3\right )-{\mathrm {e}}^{\frac {2\,x+8}{x^2}}\,\left (24\,x^4\,\mathrm {e}-96\,x^5\right )-{\mathrm {e}}^{\frac {3\,\left (2\,x+8\right )}{x^2}}\,\left (-512\,x^5+384\,\mathrm {e}\,x^4-96\,{\mathrm {e}}^2\,x^3+8\,{\mathrm {e}}^3\,x^2\right )+8\,x^5} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(100*x^2*exp((3*(2*x + 8))/x^2) + exp((2*(2*x + 8))/x^2)*(50*x + 25*x^2 + 400))/(exp((2*(2*x + 8))/x^2)*(
24*x^3*exp(2) - 192*x^4*exp(1) + 384*x^5) - exp((2*x + 8)/x^2)*(24*x^4*exp(1) - 96*x^5) - exp((3*(2*x + 8))/x^
2)*(8*x^2*exp(3) - 96*x^3*exp(2) + 384*x^4*exp(1) - 512*x^5) + 8*x^5),x)
[Out]
int(-(100*x^2*exp((3*(2*x + 8))/x^2) + exp((2*(2*x + 8))/x^2)*(50*x + 25*x^2 + 400))/(exp((2*(2*x + 8))/x^2)*(
24*x^3*exp(2) - 192*x^4*exp(1) + 384*x^5) - exp((2*x + 8)/x^2)*(24*x^4*exp(1) - 96*x^5) - exp((3*(2*x + 8))/x^
2)*(8*x^2*exp(3) - 96*x^3*exp(2) + 384*x^4*exp(1) - 512*x^5) + 8*x^5), x)
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