3.12.99 \(\int \frac {10 e^x x-10 x^2+(-25 x-10 x^2+e^x (25+10 x)) \log (5+2 x)+e^{-x^3+x^2 \log (-5 e^x+5 x)} (2 e^x-2 x+(-5 x^2+13 x^3+6 x^4+e^x (-10 x^2-4 x^3)) \log (5+2 x)+(-10 x^2-4 x^3+e^x (10 x+4 x^2)) \log (5+2 x) \log (-5 e^x+5 x))}{-5 x-2 x^2+e^x (5+2 x)} \, dx\) [1199]
Optimal. Leaf size=31 \[ \left (e^{x^2 \left (-x+\log \left (5 \left (-e^x+x\right )\right )\right )}+5 x\right ) \log (5+2 x) \]
[Out]
ln(5+2*x)*(5*x+exp((ln(-5*exp(x)+5*x)-x)*x^2))
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Rubi [F]
time = 174.01, 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 {10 e^x x-10 x^2+\left (-25 x-10 x^2+e^x (25+10 x)\right ) \log (5+2 x)+e^{-x^3+x^2 \log \left (-5 e^x+5 x\right )} \left (2 e^x-2 x+\left (-5 x^2+13 x^3+6 x^4+e^x \left (-10 x^2-4 x^3\right )\right ) \log (5+2 x)+\left (-10 x^2-4 x^3+e^x \left (10 x+4 x^2\right )\right ) \log (5+2 x) \log \left (-5 e^x+5 x\right )\right )}{-5 x-2 x^2+e^x (5+2 x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(10*E^x*x - 10*x^2 + (-25*x - 10*x^2 + E^x*(25 + 10*x))*Log[5 + 2*x] + E^(-x^3 + x^2*Log[-5*E^x + 5*x])*(2
*E^x - 2*x + (-5*x^2 + 13*x^3 + 6*x^4 + E^x*(-10*x^2 - 4*x^3))*Log[5 + 2*x] + (-10*x^2 - 4*x^3 + E^x*(10*x + 4
*x^2))*Log[5 + 2*x]*Log[-5*E^x + 5*x]))/(-5*x - 2*x^2 + E^x*(5 + 2*x)),x]
[Out]
(-25*Log[5 + 2*x])/2 + (5*(5 + 2*x)*Log[5 + 2*x])/2 + Defer[Int][(5^x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x] + 2*D
efer[Int][(5^x^2*E^(x - x^3)*(-E^x + x)^(-1 + x^2))/(-5 - 2*x), x] - 2*Log[-5*(E^x - x)]*Log[5 + 2*x]*Defer[In
t][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2), x] + Log[5 + 2*x]*Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E
^x^3, x] + 2*Log[-5*(E^x - x)]*Log[5 + 2*x]*Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x] + 2*Log[5 +
2*x]*Defer[Int][5^x^2*E^(x - x^3)*x^2*(-E^x + x)^(-1 + x^2), x] - 3*Log[5 + 2*x]*Defer[Int][(5^x^2*x^3*(-E^x
+ x)^(-1 + x^2))/E^x^3, x] - Defer[Int][(5^(1 + x^2)*(-E^x + x)^(-1 + x^2))/(E^x^3*(5 + 2*x)), x] + 2*Log[5 +
2*x]*Defer[Int][Defer[Int][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2), x], x] - 2*Log[5 + 2*x]*Defer[Int][Defer
[Int][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2), x]/(E^x - x), x] + 2*Log[5 + 2*x]*Defer[Int][(x*Defer[Int][5^
x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2), x])/(E^x - x), x] + 4*Log[-5*(E^x - x)]*Defer[Int][Defer[Int][5^x^2*E
^(x - x^3)*x*(-E^x + x)^(-1 + x^2), x]/(5 + 2*x), x] - 2*Log[5 + 2*x]*Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x +
x)^(-1 + x^2))/E^x^3, x], x] + 2*Log[5 + 2*x]*Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3,
x]/(E^x - x), x] - 2*Log[5 + 2*x]*Defer[Int][(x*Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x])/(E^x -
x), x] - 2*Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x]/(5 + 2*x), x] - 4*Log[-5*(E^x -
x)]*Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x]/(5 + 2*x), x] - 4*Defer[Int][Defer[Int][
5^x^2*E^(x - x^3)*x^2*(-E^x + x)^(-1 + x^2), x]/(5 + 2*x), x] + 6*Defer[Int][Defer[Int][(5^x^2*x^3*(-E^x + x)^
(-1 + x^2))/E^x^3, x]/(5 + 2*x), x] - 4*Defer[Int][Defer[Int][Defer[Int][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 +
x^2), x], x]/(5 + 2*x), x] + 4*Defer[Int][Defer[Int][Defer[Int][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2), x]/
(E^x - x), x]/(5 + 2*x), x] - 4*Defer[Int][Defer[Int][(x*Defer[Int][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2),
x])/(E^x - x), x]/(5 + 2*x), x] - 4*Defer[Int][Defer[Int][Defer[Int][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2
), x]/(5 + 2*x), x], x] + 4*Defer[Int][Defer[Int][Defer[Int][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2), x]/(5
+ 2*x), x]/(E^x - x), x] - 4*Defer[Int][(x*Defer[Int][Defer[Int][5^x^2*E^(x - x^3)*x*(-E^x + x)^(-1 + x^2), x]
/(5 + 2*x), x])/(E^x - x), x] + 4*Defer[Int][Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x]
, x]/(5 + 2*x), x] - 4*Defer[Int][Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x]/(E^x - x),
x]/(5 + 2*x), x] + 4*Defer[Int][Defer[Int][(x*Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x])/(E^x -
x), x]/(5 + 2*x), x] + 4*Defer[Int][Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x]/(5 + 2*x
), x], x] - 4*Defer[Int][Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x]/(5 + 2*x), x]/(E^x
- x), x] + 4*Defer[Int][(x*Defer[Int][Defer[Int][(5^x^2*x^2*(-E^x + x)^(-1 + x^2))/E^x^3, x]/(5 + 2*x), x])/(E
^x - x), x]
Rubi steps
Aborted
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Mathematica [A]
time = 0.17, size = 37, normalized size = 1.19 \begin {gather*} 5 x \log (5+2 x)+e^{-x^3} \left (-5 e^x+5 x\right )^{x^2} \log (5+2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(10*E^x*x - 10*x^2 + (-25*x - 10*x^2 + E^x*(25 + 10*x))*Log[5 + 2*x] + E^(-x^3 + x^2*Log[-5*E^x + 5*
x])*(2*E^x - 2*x + (-5*x^2 + 13*x^3 + 6*x^4 + E^x*(-10*x^2 - 4*x^3))*Log[5 + 2*x] + (-10*x^2 - 4*x^3 + E^x*(10
*x + 4*x^2))*Log[5 + 2*x]*Log[-5*E^x + 5*x]))/(-5*x - 2*x^2 + E^x*(5 + 2*x)),x]
[Out]
5*x*Log[5 + 2*x] + ((-5*E^x + 5*x)^x^2*Log[5 + 2*x])/E^x^3
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Maple [A]
time = 0.04, size = 36, normalized size = 1.16
| | |
| method |
result |
size |
| | |
| risch |
\(5 x \ln \left (5+2 x \right )+\ln \left (5+2 x \right ) \left (-5 \,{\mathrm e}^{x}+5 x \right )^{x^{2}} {\mathrm e}^{-x^{3}}\) |
\(36\) |
| | |
|
|
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|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((((4*x^2+10*x)*exp(x)-4*x^3-10*x^2)*ln(5+2*x)*ln(-5*exp(x)+5*x)+((-4*x^3-10*x^2)*exp(x)+6*x^4+13*x^3-5*x^
2)*ln(5+2*x)+2*exp(x)-2*x)*exp(x^2*ln(-5*exp(x)+5*x)-x^3)+((10*x+25)*exp(x)-10*x^2-25*x)*ln(5+2*x)+10*exp(x)*x
-10*x^2)/((5+2*x)*exp(x)-2*x^2-5*x),x,method=_RETURNVERBOSE)
[Out]
5*x*ln(5+2*x)+ln(5+2*x)*(-5*exp(x)+5*x)^(x^2)*exp(-x^3)
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((4*x^2+10*x)*exp(x)-4*x^3-10*x^2)*log(5+2*x)*log(-5*exp(x)+5*x)+((-4*x^3-10*x^2)*exp(x)+6*x^4+13*
x^3-5*x^2)*log(5+2*x)+2*exp(x)-2*x)*exp(x^2*log(-5*exp(x)+5*x)-x^3)+((10*x+25)*exp(x)-10*x^2-25*x)*log(5+2*x)+
10*exp(x)*x-10*x^2)/((5+2*x)*exp(x)-2*x^2-5*x),x, algorithm="maxima")
[Out]
5*x*log(2*x + 5) + integrate((2*(2*x^3 + 5*x^2 - (2*x^2 + 5*x)*e^x)*5^(x^2)*log(2*x + 5)*log(-x + e^x) - (((-4
*I*pi - 4*log(5) + 13)*x^3 + 6*x^4 - 5*(2*I*pi + 2*log(5) + 1)*x^2 - 2*((-2*I*pi - 2*log(5) + 5)*x^2 + 2*x^3 +
5*(-I*pi - log(5))*x)*e^x)*log(2*x + 5) - 2*x + 2*e^x)*5^(x^2))*e^(-x^3 + x^2*log(x - e^x))/(2*x^2 - (2*x + 5
)*e^x + 5*x), x)
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Fricas [A]
time = 0.35, size = 37, normalized size = 1.19 \begin {gather*} 5 \, x \log \left (2 \, x + 5\right ) + e^{\left (-x^{3} + x^{2} \log \left (5 \, x - 5 \, e^{x}\right )\right )} \log \left (2 \, x + 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((4*x^2+10*x)*exp(x)-4*x^3-10*x^2)*log(5+2*x)*log(-5*exp(x)+5*x)+((-4*x^3-10*x^2)*exp(x)+6*x^4+13*
x^3-5*x^2)*log(5+2*x)+2*exp(x)-2*x)*exp(x^2*log(-5*exp(x)+5*x)-x^3)+((10*x+25)*exp(x)-10*x^2-25*x)*log(5+2*x)+
10*exp(x)*x-10*x^2)/((5+2*x)*exp(x)-2*x^2-5*x),x, algorithm="fricas")
[Out]
5*x*log(2*x + 5) + e^(-x^3 + x^2*log(5*x - 5*e^x))*log(2*x + 5)
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Sympy [F(-1)] Timed out
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(((((4*x**2+10*x)*exp(x)-4*x**3-10*x**2)*ln(5+2*x)*ln(-5*exp(x)+5*x)+((-4*x**3-10*x**2)*exp(x)+6*x**4
+13*x**3-5*x**2)*ln(5+2*x)+2*exp(x)-2*x)*exp(x**2*ln(-5*exp(x)+5*x)-x**3)+((10*x+25)*exp(x)-10*x**2-25*x)*ln(5
+2*x)+10*exp(x)*x-10*x**2)/((5+2*x)*exp(x)-2*x**2-5*x),x)
[Out]
Timed out
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((((4*x^2+10*x)*exp(x)-4*x^3-10*x^2)*log(5+2*x)*log(-5*exp(x)+5*x)+((-4*x^3-10*x^2)*exp(x)+6*x^4+13*
x^3-5*x^2)*log(5+2*x)+2*exp(x)-2*x)*exp(x^2*log(-5*exp(x)+5*x)-x^3)+((10*x+25)*exp(x)-10*x^2-25*x)*log(5+2*x)+
10*exp(x)*x-10*x^2)/((5+2*x)*exp(x)-2*x^2-5*x),x, algorithm="giac")
[Out]
integrate((10*x^2 + (2*(2*x^3 + 5*x^2 - (2*x^2 + 5*x)*e^x)*log(5*x - 5*e^x)*log(2*x + 5) - (6*x^4 + 13*x^3 - 5
*x^2 - 2*(2*x^3 + 5*x^2)*e^x)*log(2*x + 5) + 2*x - 2*e^x)*e^(-x^3 + x^2*log(5*x - 5*e^x)) - 10*x*e^x + 5*(2*x^
2 - (2*x + 5)*e^x + 5*x)*log(2*x + 5))/(2*x^2 - (2*x + 5)*e^x + 5*x), x)
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Mupad [B]
time = 1.17, size = 30, normalized size = 0.97 \begin {gather*} \ln \left (2\,x+5\right )\,\left (5\,x+{\mathrm {e}}^{-x^3}\,{\left (5\,x-5\,{\mathrm {e}}^x\right )}^{x^2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp(x^2*log(5*x - 5*exp(x)) - x^3)*(2*x - 2*exp(x) + log(2*x + 5)*(exp(x)*(10*x^2 + 4*x^3) + 5*x^2 - 13*x
^3 - 6*x^4) + log(2*x + 5)*log(5*x - 5*exp(x))*(10*x^2 - exp(x)*(10*x + 4*x^2) + 4*x^3)) - 10*x*exp(x) + 10*x^
2 + log(2*x + 5)*(25*x - exp(x)*(10*x + 25) + 10*x^2))/(5*x - exp(x)*(2*x + 5) + 2*x^2),x)
[Out]
log(2*x + 5)*(5*x + exp(-x^3)*(5*x - 5*exp(x))^(x^2))
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