3.26.43 \(\int \frac {e^{50 x-20 x^2+2 x^3+2 (10 x-2 x^2) \log (5)+2 x \log ^2(5)} (-3+e^x-3 x)-6 x^2+e^x x^2-3 x^3+e^{25 x-10 x^2+x^3+(10 x-2 x^2) \log (5)+x \log ^2(5)} (-3+66 x-66 x^2+9 x^3+(30 x-12 x^2) \log (5)+3 x \log ^2(5)+e^x (1-23 x+20 x^2-3 x^3+(-10 x+4 x^2) \log (5)-x \log ^2(5)))}{e^{51 x-20 x^2+2 x^3+2 (10 x-2 x^2) \log (5)+2 x \log ^2(5)} x^2+e^{26 x-10 x^2+x^3+(10 x-2 x^2) \log (5)+x \log ^2(5)} (2 x^2+2 x^3)+e^x (x^2+2 x^3+x^4)} \, dx\)
Optimal. Leaf size=33 \[ \frac {-1+3 e^{-x}}{x+\frac {x}{e^{x (-5+x-\log (5))^2}+x}} \]
________________________________________________________________________________________
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^(50*x - 20*x^2 + 2*x^3 + 2*(10*x - 2*x^2)*Log[5] + 2*x*Log[5]^2)*(-3 + E^x - 3*x) - 6*x^2 + E^x*x^2 - 3
*x^3 + E^(25*x - 10*x^2 + x^3 + (10*x - 2*x^2)*Log[5] + x*Log[5]^2)*(-3 + 66*x - 66*x^2 + 9*x^3 + (30*x - 12*x
^2)*Log[5] + 3*x*Log[5]^2 + E^x*(1 - 23*x + 20*x^2 - 3*x^3 + (-10*x + 4*x^2)*Log[5] - x*Log[5]^2)))/(E^(51*x -
20*x^2 + 2*x^3 + 2*(10*x - 2*x^2)*Log[5] + 2*x*Log[5]^2)*x^2 + E^(26*x - 10*x^2 + x^3 + (10*x - 2*x^2)*Log[5]
+ x*Log[5]^2)*(2*x^2 + 2*x^3) + E^x*(x^2 + 2*x^3 + x^4)),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [F] time = 3.71, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{50 x-20 x^2+2 x^3+2 \left (10 x-2 x^2\right ) \log (5)+2 x \log ^2(5)} \left (-3+e^x-3 x\right )-6 x^2+e^x x^2-3 x^3+e^{25 x-10 x^2+x^3+\left (10 x-2 x^2\right ) \log (5)+x \log ^2(5)} \left (-3+66 x-66 x^2+9 x^3+\left (30 x-12 x^2\right ) \log (5)+3 x \log ^2(5)+e^x \left (1-23 x+20 x^2-3 x^3+\left (-10 x+4 x^2\right ) \log (5)-x \log ^2(5)\right )\right )}{e^{51 x-20 x^2+2 x^3+2 \left (10 x-2 x^2\right ) \log (5)+2 x \log ^2(5)} x^2+e^{26 x-10 x^2+x^3+\left (10 x-2 x^2\right ) \log (5)+x \log ^2(5)} \left (2 x^2+2 x^3\right )+e^x \left (x^2+2 x^3+x^4\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Integrate[(E^(50*x - 20*x^2 + 2*x^3 + 2*(10*x - 2*x^2)*Log[5] + 2*x*Log[5]^2)*(-3 + E^x - 3*x) - 6*x^2 + E^x*x
^2 - 3*x^3 + E^(25*x - 10*x^2 + x^3 + (10*x - 2*x^2)*Log[5] + x*Log[5]^2)*(-3 + 66*x - 66*x^2 + 9*x^3 + (30*x
- 12*x^2)*Log[5] + 3*x*Log[5]^2 + E^x*(1 - 23*x + 20*x^2 - 3*x^3 + (-10*x + 4*x^2)*Log[5] - x*Log[5]^2)))/(E^(
51*x - 20*x^2 + 2*x^3 + 2*(10*x - 2*x^2)*Log[5] + 2*x*Log[5]^2)*x^2 + E^(26*x - 10*x^2 + x^3 + (10*x - 2*x^2)*
Log[5] + x*Log[5]^2)*(2*x^2 + 2*x^3) + E^x*(x^2 + 2*x^3 + x^4)),x]
[Out]
Integrate[(E^(50*x - 20*x^2 + 2*x^3 + 2*(10*x - 2*x^2)*Log[5] + 2*x*Log[5]^2)*(-3 + E^x - 3*x) - 6*x^2 + E^x*x
^2 - 3*x^3 + E^(25*x - 10*x^2 + x^3 + (10*x - 2*x^2)*Log[5] + x*Log[5]^2)*(-3 + 66*x - 66*x^2 + 9*x^3 + (30*x
- 12*x^2)*Log[5] + 3*x*Log[5]^2 + E^x*(1 - 23*x + 20*x^2 - 3*x^3 + (-10*x + 4*x^2)*Log[5] - x*Log[5]^2)))/(E^(
51*x - 20*x^2 + 2*x^3 + 2*(10*x - 2*x^2)*Log[5] + 2*x*Log[5]^2)*x^2 + E^(26*x - 10*x^2 + x^3 + (10*x - 2*x^2)*
Log[5] + x*Log[5]^2)*(2*x^2 + 2*x^3) + E^x*(x^2 + 2*x^3 + x^4)), x]
________________________________________________________________________________________
fricas [B] time = 1.07, size = 254, normalized size = 7.70 \begin {gather*} -\frac {x e^{\left (3 \, x^{3} + 3 \, x \log \relax (5)^{2} - 30 \, x^{2} - 6 \, {\left (x^{2} - 5 \, x\right )} \log \relax (5) + 78 \, x\right )} - {\left (3 \, x e^{\left (x^{3} + x \log \relax (5)^{2} - 10 \, x^{2} - 2 \, {\left (x^{2} - 5 \, x\right )} \log \relax (5) + 26 \, x\right )} - e^{\left (2 \, x^{3} + 2 \, x \log \relax (5)^{2} - 20 \, x^{2} - 4 \, {\left (x^{2} - 5 \, x\right )} \log \relax (5) + 52 \, x\right )}\right )} e^{\left (2 \, x^{3} + 2 \, x \log \relax (5)^{2} - 20 \, x^{2} - 4 \, {\left (x^{2} - 5 \, x\right )} \log \relax (5) + 51 \, x\right )} - 3 \, e^{\left (4 \, x^{3} + 4 \, x \log \relax (5)^{2} - 40 \, x^{2} - 8 \, {\left (x^{2} - 5 \, x\right )} \log \relax (5) + 102 \, x\right )}}{x e^{\left (4 \, x^{3} + 4 \, x \log \relax (5)^{2} - 40 \, x^{2} - 8 \, {\left (x^{2} - 5 \, x\right )} \log \relax (5) + 103 \, x\right )} + {\left (x^{2} + x\right )} e^{\left (3 \, x^{3} + 3 \, x \log \relax (5)^{2} - 30 \, x^{2} - 6 \, {\left (x^{2} - 5 \, x\right )} \log \relax (5) + 78 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((exp(x)-3*x-3)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10*x^2+25*x)^2+((-x*log(5)^2+(4*x^2-10*x)*lo
g(5)-3*x^3+20*x^2-23*x+1)*exp(x)+3*x*log(5)^2+(-12*x^2+30*x)*log(5)+9*x^3-66*x^2+66*x-3)*exp(x*log(5)^2+(-2*x^
2+10*x)*log(5)+x^3-10*x^2+25*x)+exp(x)*x^2-3*x^3-6*x^2)/(x^2*exp(x)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10
*x^2+25*x)^2+(2*x^3+2*x^2)*exp(x)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10*x^2+25*x)+(x^4+2*x^3+x^2)*exp(x))
,x, algorithm="fricas")
[Out]
-(x*e^(3*x^3 + 3*x*log(5)^2 - 30*x^2 - 6*(x^2 - 5*x)*log(5) + 78*x) - (3*x*e^(x^3 + x*log(5)^2 - 10*x^2 - 2*(x
^2 - 5*x)*log(5) + 26*x) - e^(2*x^3 + 2*x*log(5)^2 - 20*x^2 - 4*(x^2 - 5*x)*log(5) + 52*x))*e^(2*x^3 + 2*x*log
(5)^2 - 20*x^2 - 4*(x^2 - 5*x)*log(5) + 51*x) - 3*e^(4*x^3 + 4*x*log(5)^2 - 40*x^2 - 8*(x^2 - 5*x)*log(5) + 10
2*x))/(x*e^(4*x^3 + 4*x*log(5)^2 - 40*x^2 - 8*(x^2 - 5*x)*log(5) + 103*x) + (x^2 + x)*e^(3*x^3 + 3*x*log(5)^2
- 30*x^2 - 6*(x^2 - 5*x)*log(5) + 78*x))
________________________________________________________________________________________
giac [B] time = 0.99, size = 128, normalized size = 3.88 \begin {gather*} -\frac {x e^{\left (2 \, x\right )} - 3 \, x e^{x} + e^{\left (x^{3} - 2 \, x^{2} \log \relax (5) + x \log \relax (5)^{2} - 10 \, x^{2} + 10 \, x \log \relax (5) + 27 \, x\right )} - 3 \, e^{\left (x^{3} - 2 \, x^{2} \log \relax (5) + x \log \relax (5)^{2} - 10 \, x^{2} + 10 \, x \log \relax (5) + 26 \, x\right )}}{x^{2} e^{\left (2 \, x\right )} + x e^{\left (x^{3} - 2 \, x^{2} \log \relax (5) + x \log \relax (5)^{2} - 10 \, x^{2} + 10 \, x \log \relax (5) + 27 \, x\right )} + x e^{\left (2 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((exp(x)-3*x-3)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10*x^2+25*x)^2+((-x*log(5)^2+(4*x^2-10*x)*lo
g(5)-3*x^3+20*x^2-23*x+1)*exp(x)+3*x*log(5)^2+(-12*x^2+30*x)*log(5)+9*x^3-66*x^2+66*x-3)*exp(x*log(5)^2+(-2*x^
2+10*x)*log(5)+x^3-10*x^2+25*x)+exp(x)*x^2-3*x^3-6*x^2)/(x^2*exp(x)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10
*x^2+25*x)^2+(2*x^3+2*x^2)*exp(x)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10*x^2+25*x)+(x^4+2*x^3+x^2)*exp(x))
,x, algorithm="giac")
[Out]
-(x*e^(2*x) - 3*x*e^x + e^(x^3 - 2*x^2*log(5) + x*log(5)^2 - 10*x^2 + 10*x*log(5) + 27*x) - 3*e^(x^3 - 2*x^2*l
og(5) + x*log(5)^2 - 10*x^2 + 10*x*log(5) + 26*x))/(x^2*e^(2*x) + x*e^(x^3 - 2*x^2*log(5) + x*log(5)^2 - 10*x^
2 + 10*x*log(5) + 27*x) + x*e^(2*x))
________________________________________________________________________________________
maple [A] time = 0.33, size = 56, normalized size = 1.70
|
|
|
| method |
result |
size |
|
|
|
| risch |
\(-\frac {1}{x}+\frac {3 \,{\mathrm e}^{-x}}{x}+\frac {\left ({\mathrm e}^{x}-3\right ) {\mathrm e}^{-x}}{x \left (x +\left (\frac {1}{25}\right )^{\left (x -5\right ) x} {\mathrm e}^{x \left (\ln \relax (5)^{2}+x^{2}-10 x +25\right )}+1\right )}\) |
\(56\) |
| norman |
\(\frac {\left (-{\mathrm e}^{x} x +3 x -{\mathrm e}^{x} {\mathrm e}^{x \ln \relax (5)^{2}+\left (-2 x^{2}+10 x \right ) \ln \relax (5)+x^{3}-10 x^{2}+25 x}+3 \,{\mathrm e}^{x \ln \relax (5)^{2}+\left (-2 x^{2}+10 x \right ) \ln \relax (5)+x^{3}-10 x^{2}+25 x}\right ) {\mathrm e}^{-x}}{x \left (x +{\mathrm e}^{x \ln \relax (5)^{2}+\left (-2 x^{2}+10 x \right ) \ln \relax (5)+x^{3}-10 x^{2}+25 x}+1\right )}\) |
\(122\) |
|
|
|
| |
| |
| |
| |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((exp(x)-3*x-3)*exp(x*ln(5)^2+(-2*x^2+10*x)*ln(5)+x^3-10*x^2+25*x)^2+((-x*ln(5)^2+(4*x^2-10*x)*ln(5)-3*x^3
+20*x^2-23*x+1)*exp(x)+3*x*ln(5)^2+(-12*x^2+30*x)*ln(5)+9*x^3-66*x^2+66*x-3)*exp(x*ln(5)^2+(-2*x^2+10*x)*ln(5)
+x^3-10*x^2+25*x)+exp(x)*x^2-3*x^3-6*x^2)/(x^2*exp(x)*exp(x*ln(5)^2+(-2*x^2+10*x)*ln(5)+x^3-10*x^2+25*x)^2+(2*
x^3+2*x^2)*exp(x)*exp(x*ln(5)^2+(-2*x^2+10*x)*ln(5)+x^3-10*x^2+25*x)+(x^4+2*x^3+x^2)*exp(x)),x,method=_RETURNV
ERBOSE)
[Out]
-1/x+3*exp(-x)/x+(exp(x)-3)/x*exp(-x)/(x+(1/25)^((x-5)*x)*exp(x*(ln(5)^2+x^2-10*x+25))+1)
________________________________________________________________________________________
maxima [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(((exp(x)-3*x-3)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10*x^2+25*x)^2+((-x*log(5)^2+(4*x^2-10*x)*lo
g(5)-3*x^3+20*x^2-23*x+1)*exp(x)+3*x*log(5)^2+(-12*x^2+30*x)*log(5)+9*x^3-66*x^2+66*x-3)*exp(x*log(5)^2+(-2*x^
2+10*x)*log(5)+x^3-10*x^2+25*x)+exp(x)*x^2-3*x^3-6*x^2)/(x^2*exp(x)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10
*x^2+25*x)^2+(2*x^3+2*x^2)*exp(x)*exp(x*log(5)^2+(-2*x^2+10*x)*log(5)+x^3-10*x^2+25*x)+(x^4+2*x^3+x^2)*exp(x))
,x, algorithm="maxima")
[Out]
Timed out
________________________________________________________________________________________
mupad [B] time = 1.80, size = 92, normalized size = 2.79 \begin {gather*} -\frac {{\mathrm {e}}^{-x}\,\left ({\mathrm {e}}^x-3\right )\,\left (5^{2\,x^2}\,x+5^{10\,x}\,{\mathrm {e}}^{25\,x+x\,{\ln \relax (5)}^2-10\,x^2+x^3}\right )}{x\,\left (5^{2\,x^2}\,x+5^{2\,x^2}+5^{10\,x}\,{\mathrm {e}}^{25\,x+x\,{\ln \relax (5)}^2-10\,x^2+x^3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(exp(50*x + 2*log(5)*(10*x - 2*x^2) + 2*x*log(5)^2 - 20*x^2 + 2*x^3)*(3*x - exp(x) + 3) - exp(25*x + log(
5)*(10*x - 2*x^2) + x*log(5)^2 - 10*x^2 + x^3)*(66*x + log(5)*(30*x - 12*x^2) + 3*x*log(5)^2 - exp(x)*(23*x +
log(5)*(10*x - 4*x^2) + x*log(5)^2 - 20*x^2 + 3*x^3 - 1) - 66*x^2 + 9*x^3 - 3) - x^2*exp(x) + 6*x^2 + 3*x^3)/(
exp(x)*(x^2 + 2*x^3 + x^4) + exp(25*x + log(5)*(10*x - 2*x^2) + x*log(5)^2 - 10*x^2 + x^3)*exp(x)*(2*x^2 + 2*x
^3) + x^2*exp(x)*exp(50*x + 2*log(5)*(10*x - 2*x^2) + 2*x*log(5)^2 - 20*x^2 + 2*x^3)),x)
[Out]
-(exp(-x)*(exp(x) - 3)*(5^(2*x^2)*x + 5^(10*x)*exp(25*x + x*log(5)^2 - 10*x^2 + x^3)))/(x*(5^(2*x^2)*x + 5^(2*
x^2) + 5^(10*x)*exp(25*x + x*log(5)^2 - 10*x^2 + x^3)))
________________________________________________________________________________________
sympy [B] time = 0.64, size = 63, normalized size = 1.91 \begin {gather*} \frac {e^{x} - 3}{x^{2} e^{x} + x e^{x} e^{x^{3} - 10 x^{2} + x \log {\relax (5 )}^{2} + 25 x + \left (- 2 x^{2} + 10 x\right ) \log {\relax (5 )}} + x e^{x}} - \frac {1}{x} + \frac {3 e^{- x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((exp(x)-3*x-3)*exp(x*ln(5)**2+(-2*x**2+10*x)*ln(5)+x**3-10*x**2+25*x)**2+((-x*ln(5)**2+(4*x**2-10*x
)*ln(5)-3*x**3+20*x**2-23*x+1)*exp(x)+3*x*ln(5)**2+(-12*x**2+30*x)*ln(5)+9*x**3-66*x**2+66*x-3)*exp(x*ln(5)**2
+(-2*x**2+10*x)*ln(5)+x**3-10*x**2+25*x)+exp(x)*x**2-3*x**3-6*x**2)/(x**2*exp(x)*exp(x*ln(5)**2+(-2*x**2+10*x)
*ln(5)+x**3-10*x**2+25*x)**2+(2*x**3+2*x**2)*exp(x)*exp(x*ln(5)**2+(-2*x**2+10*x)*ln(5)+x**3-10*x**2+25*x)+(x*
*4+2*x**3+x**2)*exp(x)),x)
[Out]
(exp(x) - 3)/(x**2*exp(x) + x*exp(x)*exp(x**3 - 10*x**2 + x*log(5)**2 + 25*x + (-2*x**2 + 10*x)*log(5)) + x*ex
p(x)) - 1/x + 3*exp(-x)/x
________________________________________________________________________________________