3.27.64 \(\int \frac {e^{10+5 e^3+5 e^{10}+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4} (-1-20 e^5 x^2+20 x^4)}{2 x^2} \, dx\)

Optimal. Leaf size=29 \[ e^{\frac {e^{5 \left (2+e^3+\left (-e^5+x^2\right )^2\right )}}{2 x}} \]

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Rubi [F]  time = 4.14, 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 {\exp \left (10+5 e^3+5 e^{10}+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \left (-1-20 e^5 x^2+20 x^4\right )}{2 x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(10 + 5*E^3 + 5*E^10 + E^(10 + 5*E^3 + 5*E^10 - 10*E^5*x^2 + 5*x^4)/(2*x) - 10*E^5*x^2 + 5*x^4)*(-1 - 2
0*E^5*x^2 + 20*x^4))/(2*x^2),x]

[Out]

-10*Defer[Int][E^(5*(3 + E^3 + E^10) + E^(10 + 5*E^3 + 5*E^10 - 10*E^5*x^2 + 5*x^4)/(2*x) - 10*E^5*x^2 + 5*x^4
), x] - Defer[Int][E^(10*(1 + (E^3*(1 + E^7))/2) + E^(10 + 5*E^3 + 5*E^10 - 10*E^5*x^2 + 5*x^4)/(2*x) - 10*E^5
*x^2 + 5*x^4)/x^2, x]/2 + 10*Defer[Int][E^(10*(1 + (E^3*(1 + E^7))/2) + E^(10 + 5*E^3 + 5*E^10 - 10*E^5*x^2 +
5*x^4)/(2*x) - 10*E^5*x^2 + 5*x^4)*x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {\exp \left (10+5 e^3+5 e^{10}+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \left (-1-20 e^5 x^2+20 x^4\right )}{x^2} \, dx\\ &=\frac {1}{2} \int \frac {\exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \left (-1-20 e^5 x^2+20 x^4\right )}{x^2} \, dx\\ &=\frac {1}{2} \int \left (-20 \exp \left (5+10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right )-\frac {\exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right )}{x^2}+20 \exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) x^2\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {\exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right )}{x^2} \, dx\right )-10 \int \exp \left (5+10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \, dx+10 \int \exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) x^2 \, dx\\ &=-\left (\frac {1}{2} \int \frac {\exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right )}{x^2} \, dx\right )-10 \int \exp \left (5 \left (3+e^3+e^{10}\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) \, dx+10 \int \exp \left (10 \left (1+\frac {1}{2} e^3 \left (1+e^7\right )\right )+\frac {e^{10+5 e^3+5 e^{10}-10 e^5 x^2+5 x^4}}{2 x}-10 e^5 x^2+5 x^4\right ) x^2 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.03, size = 32, normalized size = 1.10 \begin {gather*} e^{\frac {e^{5 \left (2+e^3+e^{10}-2 e^5 x^2+x^4\right )}}{2 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(10 + 5*E^3 + 5*E^10 + E^(10 + 5*E^3 + 5*E^10 - 10*E^5*x^2 + 5*x^4)/(2*x) - 10*E^5*x^2 + 5*x^4)*(
-1 - 20*E^5*x^2 + 20*x^4))/(2*x^2),x]

[Out]

E^(E^(5*(2 + E^3 + E^10 - 2*E^5*x^2 + x^4))/(2*x))

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fricas [B]  time = 0.66, size = 77, normalized size = 2.66 \begin {gather*} e^{\left (-5 \, x^{4} + 10 \, x^{2} e^{5} + \frac {10 \, x^{5} - 20 \, x^{3} e^{5} + 10 \, x e^{10} + 10 \, x e^{3} + 20 \, x + e^{\left (5 \, x^{4} - 10 \, x^{2} e^{5} + 5 \, e^{10} + 5 \, e^{3} + 10\right )}}{2 \, x} - 5 \, e^{10} - 5 \, e^{3} - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(-20*x^2*exp(5)+20*x^4-1)*exp(5*exp(5)^2-10*x^2*exp(5)+5*exp(3)+5*x^4+10)*exp(1/2*exp(5*exp(5)^2
-10*x^2*exp(5)+5*exp(3)+5*x^4+10)/x)/x^2,x, algorithm="fricas")

[Out]

e^(-5*x^4 + 10*x^2*e^5 + 1/2*(10*x^5 - 20*x^3*e^5 + 10*x*e^10 + 10*x*e^3 + 20*x + e^(5*x^4 - 10*x^2*e^5 + 5*e^
10 + 5*e^3 + 10))/x - 5*e^10 - 5*e^3 - 10)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (20 \, x^{4} - 20 \, x^{2} e^{5} - 1\right )} e^{\left (5 \, x^{4} - 10 \, x^{2} e^{5} + \frac {e^{\left (5 \, x^{4} - 10 \, x^{2} e^{5} + 5 \, e^{10} + 5 \, e^{3} + 10\right )}}{2 \, x} + 5 \, e^{10} + 5 \, e^{3} + 10\right )}}{2 \, x^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(-20*x^2*exp(5)+20*x^4-1)*exp(5*exp(5)^2-10*x^2*exp(5)+5*exp(3)+5*x^4+10)*exp(1/2*exp(5*exp(5)^2
-10*x^2*exp(5)+5*exp(3)+5*x^4+10)/x)/x^2,x, algorithm="giac")

[Out]

integrate(1/2*(20*x^4 - 20*x^2*e^5 - 1)*e^(5*x^4 - 10*x^2*e^5 + 1/2*e^(5*x^4 - 10*x^2*e^5 + 5*e^10 + 5*e^3 + 1
0)/x + 5*e^10 + 5*e^3 + 10)/x^2, x)

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maple [A]  time = 0.12, size = 30, normalized size = 1.03

method	result	size
risch	\({\mathrm e}^{\frac {{\mathrm e}^{5 \,{\mathrm e}^{10}-10 x^{2} {\mathrm e}^{5}+5 \,{\mathrm e}^{3}+5 x^{4}+10}}{2 x}}\)	\(30\)
norman	\({\mathrm e}^{\frac {{\mathrm e}^{5 \,{\mathrm e}^{10}-10 x^{2} {\mathrm e}^{5}+5 \,{\mathrm e}^{3}+5 x^{4}+10}}{2 x}}\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2*(-20*x^2*exp(5)+20*x^4-1)*exp(5*exp(5)^2-10*x^2*exp(5)+5*exp(3)+5*x^4+10)*exp(1/2*exp(5*exp(5)^2-10*x^
2*exp(5)+5*exp(3)+5*x^4+10)/x)/x^2,x,method=_RETURNVERBOSE)

[Out]

exp(1/2*exp(5*exp(10)-10*x^2*exp(5)+5*exp(3)+5*x^4+10)/x)

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maxima [A]  time = 1.19, size = 29, normalized size = 1.00 \begin {gather*} e^{\left (\frac {e^{\left (5 \, x^{4} - 10 \, x^{2} e^{5} + 5 \, e^{10} + 5 \, e^{3} + 10\right )}}{2 \, x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(-20*x^2*exp(5)+20*x^4-1)*exp(5*exp(5)^2-10*x^2*exp(5)+5*exp(3)+5*x^4+10)*exp(1/2*exp(5*exp(5)^2
-10*x^2*exp(5)+5*exp(3)+5*x^4+10)/x)/x^2,x, algorithm="maxima")

[Out]

e^(1/2*e^(5*x^4 - 10*x^2*e^5 + 5*e^10 + 5*e^3 + 10)/x)

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mupad [B]  time = 1.77, size = 32, normalized size = 1.10 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{-10\,x^2\,{\mathrm {e}}^5}\,{\mathrm {e}}^{5\,{\mathrm {e}}^3}\,{\mathrm {e}}^{5\,{\mathrm {e}}^{10}}\,{\mathrm {e}}^{10}\,{\mathrm {e}}^{5\,x^4}}{2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(5*exp(3) + 5*exp(10) - 10*x^2*exp(5) + 5*x^4 + 10)*exp(exp(5*exp(3) + 5*exp(10) - 10*x^2*exp(5) + 5*
x^4 + 10)/(2*x))*(20*x^2*exp(5) - 20*x^4 + 1))/(2*x^2),x)

[Out]

exp((exp(-10*x^2*exp(5))*exp(5*exp(3))*exp(5*exp(10))*exp(10)*exp(5*x^4))/(2*x))

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sympy [A]  time = 0.45, size = 31, normalized size = 1.07 \begin {gather*} e^{\frac {e^{5 x^{4} - 10 x^{2} e^{5} + 10 + 5 e^{3} + 5 e^{10}}}{2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(-20*x**2*exp(5)+20*x**4-1)*exp(5*exp(5)**2-10*x**2*exp(5)+5*exp(3)+5*x**4+10)*exp(1/2*exp(5*exp
(5)**2-10*x**2*exp(5)+5*exp(3)+5*x**4+10)/x)/x**2,x)

[Out]

exp(exp(5*x**4 - 10*x**2*exp(5) + 10 + 5*exp(3) + 5*exp(10))/(2*x))

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