3.87.55 \(\int \frac {1}{7} e^{\frac {1}{7} (e^{e^x-x} (-28+7 e^{4 x}-x)+35 x-7 e^{4 x} x+x^2)} (35+e^{4 x} (-7-28 x)+2 x+e^{e^x-x} (27+e^{4 x} (21+7 e^x)+e^x (-28-x)+x)) \, dx\)

Optimal. Leaf size=30 \[ e^{\left (e^{e^x-x}-x\right ) \left (-4+e^{4 x}-\frac {x}{7}\right )+x} \]

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Rubi [F]  time = 9.34, 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 {1}{7} \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \left (35+e^{4 x} (-7-28 x)+2 x+e^{e^x-x} \left (27+e^{4 x} \left (21+7 e^x\right )+e^x (-28-x)+x\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7)*(35 + E^(4*x)*(-7 - 28*x) + 2*x + E^
(E^x - x)*(27 + E^(4*x)*(21 + 7*E^x) + E^x*(-28 - x) + x)))/7,x]

[Out]

5*Defer[Int][E^((E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7), x] - 4*Defer[Int][E^(E^x +
(E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7), x] + (27*Defer[Int][E^(E^x - x + (E^(E^x -
x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7), x])/7 + 3*Defer[Int][E^(E^x + 3*x + (E^(E^x - x)*(-28
+ 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7), x] - Defer[Int][E^(4*x + (E^(E^x - x)*(-28 + 7*E^(4*x) - x)
+ 35*x - 7*E^(4*x)*x + x^2)/7), x] + Defer[Int][E^(E^x + 4*x + (E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E
^(4*x)*x + x^2)/7), x] + (2*Defer[Int][E^((E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7)*x,
x])/7 - Defer[Int][E^(E^x + (E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7)*x, x]/7 + Defer
[Int][E^(E^x - x + (E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7)*x, x]/7 - 4*Defer[Int][E^
(4*x + (E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{7} \int \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \left (35+e^{4 x} (-7-28 x)+2 x+e^{e^x-x} \left (27+e^{4 x} \left (21+7 e^x\right )+e^x (-28-x)+x\right )\right ) \, dx\\ &=\frac {1}{7} \int \left (35 \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right )+2 \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x-7 \exp \left (4 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) (1+4 x)+\exp \left (e^x-x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \left (27-28 e^x+21 e^{4 x}+7 e^{5 x}+x-e^x x\right )\right ) \, dx\\ &=\frac {1}{7} \int \exp \left (e^x-x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \left (27-28 e^x+21 e^{4 x}+7 e^{5 x}+x-e^x x\right ) \, dx+\frac {2}{7} \int \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x \, dx+5 \int \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \, dx-\int \exp \left (4 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) (1+4 x) \, dx\\ &=\frac {1}{7} \int \left (-28 \exp \left (e^x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right )+27 \exp \left (e^x-x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right )+21 \exp \left (e^x+3 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right )+7 \exp \left (e^x+4 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right )-\exp \left (e^x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x+\exp \left (e^x-x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x\right ) \, dx+\frac {2}{7} \int \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x \, dx+5 \int \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \, dx-\int \left (\exp \left (4 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right )+4 \exp \left (4 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x\right ) \, dx\\ &=-\left (\frac {1}{7} \int \exp \left (e^x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x \, dx\right )+\frac {1}{7} \int \exp \left (e^x-x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x \, dx+\frac {2}{7} \int \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x \, dx+3 \int \exp \left (e^x+3 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \, dx+\frac {27}{7} \int \exp \left (e^x-x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \, dx-4 \int \exp \left (e^x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \, dx-4 \int \exp \left (4 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) x \, dx+5 \int \exp \left (\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \, dx-\int \exp \left (4 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \, dx+\int \exp \left (e^x+4 x+\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.19, size = 43, normalized size = 1.43 \begin {gather*} e^{\frac {1}{7} \left (e^{e^x-x} \left (-28+7 e^{4 x}-x\right )+35 x-7 e^{4 x} x+x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7)*(35 + E^(4*x)*(-7 - 28*x) + 2*
x + E^(E^x - x)*(27 + E^(4*x)*(21 + 7*E^x) + E^x*(-28 - x) + x)))/7,x]

[Out]

E^((E^(E^x - x)*(-28 + 7*E^(4*x) - x) + 35*x - 7*E^(4*x)*x + x^2)/7)

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fricas [A]  time = 0.55, size = 35, normalized size = 1.17 \begin {gather*} e^{\left (\frac {1}{7} \, x^{2} - x e^{\left (4 \, x\right )} - \frac {1}{7} \, {\left (x - 7 \, e^{\left (4 \, x\right )} + 28\right )} e^{\left (-x + e^{x}\right )} + 5 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/7*(((7*exp(x)+21)*exp(4*x)+(-x-28)*exp(x)+x+27)*exp(exp(x)-x)+(-28*x-7)*exp(4*x)+2*x+35)*exp(1/7*(
7*exp(4*x)-x-28)*exp(exp(x)-x)-x*exp(4*x)+1/7*x^2+5*x),x, algorithm="fricas")

[Out]

e^(1/7*x^2 - x*e^(4*x) - 1/7*(x - 7*e^(4*x) + 28)*e^(-x + e^x) + 5*x)

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giac [A]  time = 0.40, size = 43, normalized size = 1.43 \begin {gather*} e^{\left (\frac {1}{7} \, x^{2} - x e^{\left (4 \, x\right )} - \frac {1}{7} \, x e^{\left (-x + e^{x}\right )} + 5 \, x + e^{\left (3 \, x + e^{x}\right )} - 4 \, e^{\left (-x + e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/7*(((7*exp(x)+21)*exp(4*x)+(-x-28)*exp(x)+x+27)*exp(exp(x)-x)+(-28*x-7)*exp(4*x)+2*x+35)*exp(1/7*(
7*exp(4*x)-x-28)*exp(exp(x)-x)-x*exp(4*x)+1/7*x^2+5*x),x, algorithm="giac")

[Out]

e^(1/7*x^2 - x*e^(4*x) - 1/7*x*e^(-x + e^x) + 5*x + e^(3*x + e^x) - 4*e^(-x + e^x))

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maple [A]  time = 0.13, size = 44, normalized size = 1.47

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{3 x +{\mathrm e}^{x}}-\frac {{\mathrm e}^{{\mathrm e}^{x}-x} x}{7}-4 \,{\mathrm e}^{{\mathrm e}^{x}-x}-x \,{\mathrm e}^{4 x}+\frac {x^{2}}{7}+5 x}\)	\(44\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/7*(((7*exp(x)+21)*exp(4*x)+(-x-28)*exp(x)+x+27)*exp(exp(x)-x)+(-28*x-7)*exp(4*x)+2*x+35)*exp(1/7*(7*exp(
4*x)-x-28)*exp(exp(x)-x)-x*exp(4*x)+1/7*x^2+5*x),x,method=_RETURNVERBOSE)

[Out]

exp(exp(3*x+exp(x))-1/7*exp(exp(x)-x)*x-4*exp(exp(x)-x)-x*exp(4*x)+1/7*x^2+5*x)

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maxima [A]  time = 0.74, size = 43, normalized size = 1.43 \begin {gather*} e^{\left (\frac {1}{7} \, x^{2} - x e^{\left (4 \, x\right )} - \frac {1}{7} \, x e^{\left (-x + e^{x}\right )} + 5 \, x + e^{\left (3 \, x + e^{x}\right )} - 4 \, e^{\left (-x + e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/7*(((7*exp(x)+21)*exp(4*x)+(-x-28)*exp(x)+x+27)*exp(exp(x)-x)+(-28*x-7)*exp(4*x)+2*x+35)*exp(1/7*(
7*exp(4*x)-x-28)*exp(exp(x)-x)-x*exp(4*x)+1/7*x^2+5*x),x, algorithm="maxima")

[Out]

e^(1/7*x^2 - x*e^(4*x) - 1/7*x*e^(-x + e^x) + 5*x + e^(3*x + e^x) - 4*e^(-x + e^x))

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mupad [B]  time = 5.48, size = 49, normalized size = 1.63 \begin {gather*} {\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{\frac {x^2}{7}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^x}}{7}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(5*x - x*exp(4*x) - (exp(exp(x) - x)*(x - 7*exp(4*x) + 28))/7 + x^2/7)*(2*x - exp(4*x)*(28*x + 7) + ex
p(exp(x) - x)*(x - exp(x)*(x + 28) + exp(4*x)*(7*exp(x) + 21) + 27) + 35))/7,x)

[Out]

exp(5*x)*exp(exp(3*x)*exp(exp(x)))*exp(-4*exp(-x)*exp(exp(x)))*exp(-x*exp(4*x))*exp(x^2/7)*exp(-(x*exp(-x)*exp
(exp(x)))/7)

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sympy [A]  time = 0.81, size = 32, normalized size = 1.07 \begin {gather*} e^{\frac {x^{2}}{7} - x e^{4 x} + 5 x + \left (- \frac {x}{7} + e^{4 x} - 4\right ) e^{- x + e^{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/7*(((7*exp(x)+21)*exp(4*x)+(-x-28)*exp(x)+x+27)*exp(exp(x)-x)+(-28*x-7)*exp(4*x)+2*x+35)*exp(1/7*(
7*exp(4*x)-x-28)*exp(exp(x)-x)-x*exp(4*x)+1/7*x**2+5*x),x)

[Out]

exp(x**2/7 - x*exp(4*x) + 5*x + (-x/7 + exp(4*x) - 4)*exp(-x + exp(x)))

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