3.51.26 \(\int \frac {4 e^{10}+e^{e^{4-4 x+x^2}-x} (-2 e^5+e^{9-4 x+x^2} (-8+4 x))}{4 e^{2 e^{4-4 x+x^2}-2 x}+e^{5+e^{4-4 x+x^2}-x} (44+16 x)+e^{10} (121+88 x+16 x^2)} \, dx\)
Optimal. Leaf size=28 \[ \frac {1}{5-2 \left (e^{-5+e^{(2-x)^2}-x}+2 (4+x)\right )} \]
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Rubi [F] time = 6.82, 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 {4 e^{10}+e^{e^{4-4 x+x^2}-x} \left (-2 e^5+e^{9-4 x+x^2} (-8+4 x)\right )}{4 e^{2 e^{4-4 x+x^2}-2 x}+e^{5+e^{4-4 x+x^2}-x} (44+16 x)+e^{10} \left (121+88 x+16 x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(4*E^10 + E^(E^(4 - 4*x + x^2) - x)*(-2*E^5 + E^(9 - 4*x + x^2)*(-8 + 4*x)))/(4*E^(2*E^(4 - 4*x + x^2) - 2
*x) + E^(5 + E^(4 - 4*x + x^2) - x)*(44 + 16*x) + E^10*(121 + 88*x + 16*x^2)),x]
[Out]
-2*Defer[Int][E^(5 + E^(-2 + x)^2 + x)/(2*E^E^(-2 + x)^2 + 11*E^(5 + x) + 4*E^(5 + x)*x)^2, x] - 8*Defer[Int][
E^(9 + E^(-2 + x)^2 - 3*x + x^2)/(2*E^E^(-2 + x)^2 + 11*E^(5 + x) + 4*E^(5 + x)*x)^2, x] + 4*Defer[Int][(E^(9
+ E^(-2 + x)^2 - 3*x + x^2)*x)/(2*E^E^(-2 + x)^2 + 11*E^(5 + x) + 4*E^(5 + x)*x)^2, x] - 8*Defer[Int][E^(5 + E
^(-2 + x)^2 + x)/((11 + 4*x)*(2*E^E^(-2 + x)^2 + 11*E^(5 + x) + 4*E^(5 + x)*x)^2), x] + 4*Defer[Int][E^(5 + x)
/((11 + 4*x)*(2*E^E^(-2 + x)^2 + 11*E^(5 + x) + 4*E^(5 + x)*x)), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 e^{2 (5+x)}-2 e^{5+e^{(-2+x)^2}+x}+4 e^{9+e^{(-2+x)^2}-3 x+x^2} (-2+x)}{\left (2 e^{e^{(-2+x)^2}}+e^{5+x} (11+4 x)\right )^2} \, dx\\ &=\int \left (\frac {2 e^{5+x} \left (-e^{e^{(-2+x)^2}}+2 e^{5+x}\right )}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2}+\frac {4 e^{9+e^{(-2+x)^2}-3 x+x^2} (-2+x)}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2}\right ) \, dx\\ &=2 \int \frac {e^{5+x} \left (-e^{e^{(-2+x)^2}}+2 e^{5+x}\right )}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx+4 \int \frac {e^{9+e^{(-2+x)^2}-3 x+x^2} (-2+x)}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx\\ &=2 \int \left (-\frac {e^{5+e^{(-2+x)^2}+x} (15+4 x)}{(11+4 x) \left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2}+\frac {2 e^{5+x}}{(11+4 x) \left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )}\right ) \, dx+4 \int \left (-\frac {2 e^{9+e^{(-2+x)^2}-3 x+x^2}}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2}+\frac {e^{9+e^{(-2+x)^2}-3 x+x^2} x}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2}\right ) \, dx\\ &=-\left (2 \int \frac {e^{5+e^{(-2+x)^2}+x} (15+4 x)}{(11+4 x) \left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx\right )+4 \int \frac {e^{9+e^{(-2+x)^2}-3 x+x^2} x}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx+4 \int \frac {e^{5+x}}{(11+4 x) \left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )} \, dx-8 \int \frac {e^{9+e^{(-2+x)^2}-3 x+x^2}}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx\\ &=-\left (2 \int \left (\frac {e^{5+e^{(-2+x)^2}+x}}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2}+\frac {4 e^{5+e^{(-2+x)^2}+x}}{(11+4 x) \left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2}\right ) \, dx\right )+4 \int \frac {e^{9+e^{(-2+x)^2}-3 x+x^2} x}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx+4 \int \frac {e^{5+x}}{(11+4 x) \left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )} \, dx-8 \int \frac {e^{9+e^{(-2+x)^2}-3 x+x^2}}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx\\ &=-\left (2 \int \frac {e^{5+e^{(-2+x)^2}+x}}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx\right )+4 \int \frac {e^{9+e^{(-2+x)^2}-3 x+x^2} x}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx+4 \int \frac {e^{5+x}}{(11+4 x) \left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )} \, dx-8 \int \frac {e^{9+e^{(-2+x)^2}-3 x+x^2}}{\left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx-8 \int \frac {e^{5+e^{(-2+x)^2}+x}}{(11+4 x) \left (2 e^{e^{(-2+x)^2}}+11 e^{5+x}+4 e^{5+x} x\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 32, normalized size = 1.14 \begin {gather*} -\frac {e^{5+x}}{2 e^{e^{(-2+x)^2}}+e^{5+x} (11+4 x)} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(4*E^10 + E^(E^(4 - 4*x + x^2) - x)*(-2*E^5 + E^(9 - 4*x + x^2)*(-8 + 4*x)))/(4*E^(2*E^(4 - 4*x + x^
2) - 2*x) + E^(5 + E^(4 - 4*x + x^2) - x)*(44 + 16*x) + E^10*(121 + 88*x + 16*x^2)),x]
[Out]
-(E^(5 + x)/(2*E^E^(-2 + x)^2 + E^(5 + x)*(11 + 4*x)))
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fricas [A] time = 0.72, size = 40, normalized size = 1.43 \begin {gather*} -\frac {e^{10}}{{\left (4 \, x + 11\right )} e^{10} + 2 \, e^{\left (-{\left ({\left (x - 5\right )} e^{5} - e^{\left (x^{2} - 4 \, x + 9\right )}\right )} e^{\left (-5\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x-8)*exp(5)*exp(x^2-4*x+4)-2*exp(5))*exp(exp(x^2-4*x+4)-x)+4*exp(5)^2)/(4*exp(exp(x^2-4*x+4)-x)
^2+(16*x+44)*exp(5)*exp(exp(x^2-4*x+4)-x)+(16*x^2+88*x+121)*exp(5)^2),x, algorithm="fricas")
[Out]
-e^10/((4*x + 11)*e^10 + 2*e^(-((x - 5)*e^5 - e^(x^2 - 4*x + 9))*e^(-5)))
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giac [B] time = 2.09, size = 2593, normalized size = 92.61 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x-8)*exp(5)*exp(x^2-4*x+4)-2*exp(5))*exp(exp(x^2-4*x+4)-x)+4*exp(5)^2)/(4*exp(exp(x^2-4*x+4)-x)
^2+(16*x+44)*exp(5)*exp(exp(x^2-4*x+4)-x)+(16*x^2+88*x+121)*exp(5)^2),x, algorithm="giac")
[Out]
-(1024*x^6*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) + 7168*x^5*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) +
1024*x^5*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) - 1024*x^5*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19) + 5
504*x^4*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) + 4352*x^4*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) + 2
56*x^4*e^(2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13) - 10240*x^4*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19) - 10
24*x^4*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 14) + 256*x^4*e^(19/2*x + e^(x^2 - 4*x + 4) + 15) - 55616*x^3*e^
(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) - 6464*x^3*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) + 384*x^3*e^(
2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13) - 30336*x^3*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19) - 7424*x^3*e^(
x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 14) - 256*x^3*e^(x^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9) + 3328*x^3*e^(19/2
*x + e^(x^2 - 4*x + 4) + 15) + 256*x^3*e^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) - 96316*x^2*e^(2*x^2 + 3/2*x + e^
(x^2 - 4*x + 4) + 23) - 37840*x^2*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) - 2672*x^2*e^(2*x^2 - 1/2*x + 3
*e^(x^2 - 4*x + 4) + 13) + 1408*x^2*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19) - 9920*x^2*e^(x^2 + 9/2*x + 2*e^
(x^2 - 4*x + 4) + 14) - 1152*x^2*e^(x^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9) + 16096*x^2*e^(19/2*x + e^(x^2 - 4*
x + 4) + 15) + 2624*x^2*e^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) + 64*x^2*e^(15/2*x + 3*e^(x^2 - 4*x + 4) + 5) +
106480*x*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) + 7744*x*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) - 21
12*x*e^(2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13) + 136972*x*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19) + 28688
*x*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 14) + 688*x*e^(x^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9) + 34320*x*e^(1
9/2*x + e^(x^2 - 4*x + 4) + 15) + 8880*x*e^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) + 480*x*e^(15/2*x + 3*e^(x^2 -
4*x + 4) + 5) + 234256*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) + 85184*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x +
4) + 18) + 7744*e^(2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13) + 159720*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19
) + 58080*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 14) + 5280*e^(x^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9) + 27225*
e^(19/2*x + e^(x^2 - 4*x + 4) + 15) + 9900*e^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) + 900*e^(15/2*x + 3*e^(x^2 -
4*x + 4) + 5))/(4096*x^7*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) + 39936*x^6*e^(2*x^2 + 3/2*x + e^(x^2 - 4*
x + 4) + 23) + 6144*x^6*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) - 4096*x^6*e^(x^2 + 11/2*x + e^(x^2 - 4*x
+ 4) + 19) + 100864*x^5*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) + 43008*x^5*e^(2*x^2 + 1/2*x + 2*e^(x^2 -
4*x + 4) + 18) + 3072*x^5*e^(2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13) - 52224*x^5*e^(x^2 + 11/2*x + e^(x^2 -
4*x + 4) + 19) - 6144*x^5*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 14) + 1024*x^5*e^(19/2*x + e^(x^2 - 4*x + 4)
+ 15) - 161920*x^4*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) + 33024*x^4*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x +
4) + 18) + 13056*x^4*e^(2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13) + 512*x^4*e^(2*x^2 - 3/2*x + 4*e^(x^2 - 4*x
+ 4) + 8) - 233984*x^4*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19) - 61440*x^4*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x +
4) + 14) - 3072*x^4*e^(x^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9) + 16128*x^4*e^(19/2*x + e^(x^2 - 4*x + 4) + 15)
+ 1536*x^4*e^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) - 997040*x^3*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) - 33
3696*x^3*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) - 19392*x^3*e^(2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13)
+ 768*x^3*e^(2*x^2 - 3/2*x + 4*e^(x^2 - 4*x + 4) + 8) - 328064*x^3*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19)
- 182016*x^3*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 14) - 22272*x^3*e^(x^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9)
- 512*x^3*e^(x^2 + 5/2*x + 4*e^(x^2 - 4*x + 4) + 4) + 100992*x^3*e^(19/2*x + e^(x^2 - 4*x + 4) + 15) + 19968*x
^3*e^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) + 768*x^3*e^(15/2*x + 3*e^(x^2 - 4*x + 4) + 5) - 633556*x^2*e^(2*x^2
+ 3/2*x + e^(x^2 - 4*x + 4) + 23) - 577896*x^2*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) - 113520*x^2*e^(2*
x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13) - 5344*x^2*e^(2*x^2 - 3/2*x + 4*e^(x^2 - 4*x + 4) + 8) + 563376*x^2*e^
(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19) + 8448*x^2*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 14) - 29760*x^2*e^(x
^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9) - 2304*x^2*e^(x^2 + 5/2*x + 4*e^(x^2 - 4*x + 4) + 4) + 314336*x^2*e^(19/
2*x + e^(x^2 - 4*x + 4) + 15) + 96576*x^2*e^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) + 7872*x^2*e^(15/2*x + 3*e^(x^
2 - 4*x + 4) + 5) + 128*x^2*e^(13/2*x + 4*e^(x^2 - 4*x + 4)) + 2108304*x*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4)
+ 23) + 638880*x*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*x + 4) + 18) + 23232*x*e^(2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4)
+ 13) - 4224*x*e^(2*x^2 - 3/2*x + 4*e^(x^2 - 4*x + 4) + 8) + 2145572*x*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) +
19) + 821832*x*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 14) + 86064*x*e^(x^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9)
+ 1376*x*e^(x^2 + 5/2*x + 4*e^(x^2 - 4*x + 4) + 4) + 486420*x*e^(19/2*x + e^(x^2 - 4*x + 4) + 15) + 205920*x*e
^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) + 26640*x*e^(15/2*x + 3*e^(x^2 - 4*x + 4) + 5) + 960*x*e^(13/2*x + 4*e^(x
^2 - 4*x + 4)) + 2576816*e^(2*x^2 + 3/2*x + e^(x^2 - 4*x + 4) + 23) + 1405536*e^(2*x^2 + 1/2*x + 2*e^(x^2 - 4*
x + 4) + 18) + 255552*e^(2*x^2 - 1/2*x + 3*e^(x^2 - 4*x + 4) + 13) + 15488*e^(2*x^2 - 3/2*x + 4*e^(x^2 - 4*x +
4) + 8) + 1756920*e^(x^2 + 11/2*x + e^(x^2 - 4*x + 4) + 19) + 958320*e^(x^2 + 9/2*x + 2*e^(x^2 - 4*x + 4) + 1
4) + 174240*e^(x^2 + 7/2*x + 3*e^(x^2 - 4*x + 4) + 9) + 10560*e^(x^2 + 5/2*x + 4*e^(x^2 - 4*x + 4) + 4) + 2994
75*e^(19/2*x + e^(x^2 - 4*x + 4) + 15) + 163350*e^(17/2*x + 2*e^(x^2 - 4*x + 4) + 10) + 29700*e^(15/2*x + 3*e^
(x^2 - 4*x + 4) + 5) + 1800*e^(13/2*x + 4*e^(x^2 - 4*x + 4)))
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maple [A] time = 0.24, size = 30, normalized size = 1.07
|
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| method |
result |
size |
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| risch |
\(-\frac {{\mathrm e}^{5}}{4 x \,{\mathrm e}^{5}+11 \,{\mathrm e}^{5}+2 \,{\mathrm e}^{{\mathrm e}^{\left (x -2\right )^{2}}-x}}\) |
\(30\) |
| norman |
\(-\frac {{\mathrm e}^{5}}{4 x \,{\mathrm e}^{5}+11 \,{\mathrm e}^{5}+2 \,{\mathrm e}^{{\mathrm e}^{x^{2}-4 x +4}-x}}\) |
\(33\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((4*x-8)*exp(5)*exp(x^2-4*x+4)-2*exp(5))*exp(exp(x^2-4*x+4)-x)+4*exp(5)^2)/(4*exp(exp(x^2-4*x+4)-x)^2+(16
*x+44)*exp(5)*exp(exp(x^2-4*x+4)-x)+(16*x^2+88*x+121)*exp(5)^2),x,method=_RETURNVERBOSE)
[Out]
-exp(5)/(4*x*exp(5)+11*exp(5)+2*exp(exp((x-2)^2)-x))
________________________________________________________________________________________
maxima [A] time = 0.40, size = 34, normalized size = 1.21 \begin {gather*} -\frac {e^{\left (x + 5\right )}}{{\left (4 \, x e^{5} + 11 \, e^{5}\right )} e^{x} + 2 \, e^{\left (e^{\left (x^{2} - 4 \, x + 4\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x-8)*exp(5)*exp(x^2-4*x+4)-2*exp(5))*exp(exp(x^2-4*x+4)-x)+4*exp(5)^2)/(4*exp(exp(x^2-4*x+4)-x)
^2+(16*x+44)*exp(5)*exp(exp(x^2-4*x+4)-x)+(16*x^2+88*x+121)*exp(5)^2),x, algorithm="maxima")
[Out]
-e^(x + 5)/((4*x*e^5 + 11*e^5)*e^x + 2*e^(e^(x^2 - 4*x + 4)))
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {4\,{\mathrm {e}}^{10}-{\mathrm {e}}^{{\mathrm {e}}^{x^2-4\,x+4}-x}\,\left (2\,{\mathrm {e}}^5-{\mathrm {e}}^5\,{\mathrm {e}}^{x^2-4\,x+4}\,\left (4\,x-8\right )\right )}{4\,{\mathrm {e}}^{2\,{\mathrm {e}}^{x^2-4\,x+4}-2\,x}+{\mathrm {e}}^{10}\,\left (16\,x^2+88\,x+121\right )+{\mathrm {e}}^{{\mathrm {e}}^{x^2-4\,x+4}-x}\,{\mathrm {e}}^5\,\left (16\,x+44\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((4*exp(10) - exp(exp(x^2 - 4*x + 4) - x)*(2*exp(5) - exp(5)*exp(x^2 - 4*x + 4)*(4*x - 8)))/(4*exp(2*exp(x^
2 - 4*x + 4) - 2*x) + exp(10)*(88*x + 16*x^2 + 121) + exp(exp(x^2 - 4*x + 4) - x)*exp(5)*(16*x + 44)),x)
[Out]
int((4*exp(10) - exp(exp(x^2 - 4*x + 4) - x)*(2*exp(5) - exp(5)*exp(x^2 - 4*x + 4)*(4*x - 8)))/(4*exp(2*exp(x^
2 - 4*x + 4) - 2*x) + exp(10)*(88*x + 16*x^2 + 121) + exp(exp(x^2 - 4*x + 4) - x)*exp(5)*(16*x + 44)), x)
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sympy [A] time = 0.36, size = 31, normalized size = 1.11 \begin {gather*} - \frac {e^{5}}{4 x e^{5} + 2 e^{- x + e^{x^{2} - 4 x + 4}} + 11 e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x-8)*exp(5)*exp(x**2-4*x+4)-2*exp(5))*exp(exp(x**2-4*x+4)-x)+4*exp(5)**2)/(4*exp(exp(x**2-4*x+4
)-x)**2+(16*x+44)*exp(5)*exp(exp(x**2-4*x+4)-x)+(16*x**2+88*x+121)*exp(5)**2),x)
[Out]
-exp(5)/(4*x*exp(5) + 2*exp(-x + exp(x**2 - 4*x + 4)) + 11*exp(5))
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