3.91.59 \(\int \frac {1}{8} e^{16+\frac {1}{8} e^{-e^{16+7 x+x^2}}-e^{16+7 x+x^2}+7 x+x^2} (-7-2 x) \, dx\)

Optimal. Leaf size=23 \[ e^{\frac {1}{8} e^{-e^{(-4-x)^2-x}}} \]

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Rubi [F]  time = 0.48, 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}{8} \exp \left (16+\frac {1}{8} e^{-e^{16+7 x+x^2}}-e^{16+7 x+x^2}+7 x+x^2\right ) (-7-2 x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(16 + 1/(8*E^E^(16 + 7*x + x^2)) - E^(16 + 7*x + x^2) + 7*x + x^2)*(-7 - 2*x))/8,x]

[Out]

(-7*Defer[Int][E^(16 + 1/(8*E^E^(16 + 7*x + x^2)) - E^(16 + 7*x + x^2) + 7*x + x^2), x])/8 - Defer[Int][E^(16
+ 1/(8*E^E^(16 + 7*x + x^2)) - E^(16 + 7*x + x^2) + 7*x + x^2)*x, x]/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int \exp \left (16+\frac {1}{8} e^{-e^{16+7 x+x^2}}-e^{16+7 x+x^2}+7 x+x^2\right ) (-7-2 x) \, dx\\ &=\frac {1}{8} \int \left (-7 \exp \left (16+\frac {1}{8} e^{-e^{16+7 x+x^2}}-e^{16+7 x+x^2}+7 x+x^2\right )-2 \exp \left (16+\frac {1}{8} e^{-e^{16+7 x+x^2}}-e^{16+7 x+x^2}+7 x+x^2\right ) x\right ) \, dx\\ &=-\left (\frac {1}{4} \int \exp \left (16+\frac {1}{8} e^{-e^{16+7 x+x^2}}-e^{16+7 x+x^2}+7 x+x^2\right ) x \, dx\right )-\frac {7}{8} \int \exp \left (16+\frac {1}{8} e^{-e^{16+7 x+x^2}}-e^{16+7 x+x^2}+7 x+x^2\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 20, normalized size = 0.87 \begin {gather*} e^{\frac {1}{8} e^{-e^{16+7 x+x^2}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(16 + 1/(8*E^E^(16 + 7*x + x^2)) - E^(16 + 7*x + x^2) + 7*x + x^2)*(-7 - 2*x))/8,x]

[Out]

E^(1/(8*E^E^(16 + 7*x + x^2)))

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fricas [A]  time = 0.55, size = 20, normalized size = 0.87 \begin {gather*} e^{\left (\frac {1}{2} \, e^{\left (-e^{\left (x^{2} + 7 \, x + 16\right )} - 2 \, \log \relax (2)\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(-2*x-7)*exp(x^2+7*x+16)*exp(1/2/exp(exp(x^2+7*x+16)+2*log(2)))/exp(exp(x^2+7*x+16)+2*log(2)),x,
algorithm="fricas")

[Out]

e^(1/2*e^(-e^(x^2 + 7*x + 16) - 2*log(2)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {1}{2} \, {\left (2 \, x + 7\right )} e^{\left (x^{2} + 7 \, x - e^{\left (x^{2} + 7 \, x + 16\right )} + \frac {1}{2} \, e^{\left (-e^{\left (x^{2} + 7 \, x + 16\right )} - 2 \, \log \relax (2)\right )} - 2 \, \log \relax (2) + 16\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(-2*x-7)*exp(x^2+7*x+16)*exp(1/2/exp(exp(x^2+7*x+16)+2*log(2)))/exp(exp(x^2+7*x+16)+2*log(2)),x,
algorithm="giac")

[Out]

integrate(-1/2*(2*x + 7)*e^(x^2 + 7*x - e^(x^2 + 7*x + 16) + 1/2*e^(-e^(x^2 + 7*x + 16) - 2*log(2)) - 2*log(2)
+ 16), x)

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maple [A]  time = 0.11, size = 16, normalized size = 0.70

method	result	size
risch	\({\mathrm e}^{\frac {{\mathrm e}^{-{\mathrm e}^{x^{2}+7 x +16}}}{8}}\)	\(16\)
norman	\({\mathrm e}^{\frac {{\mathrm e}^{-{\mathrm e}^{x^{2}+7 x +16}}}{8}}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2*(-2*x-7)*exp(x^2+7*x+16)*exp(1/2/exp(exp(x^2+7*x+16)+2*ln(2)))/exp(exp(x^2+7*x+16)+2*ln(2)),x,method=_
RETURNVERBOSE)

[Out]

exp(1/8*exp(-exp(x^2+7*x+16)))

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maxima [A]  time = 0.72, size = 15, normalized size = 0.65 \begin {gather*} e^{\left (\frac {1}{8} \, e^{\left (-e^{\left (x^{2} + 7 \, x + 16\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(-2*x-7)*exp(x^2+7*x+16)*exp(1/2/exp(exp(x^2+7*x+16)+2*log(2)))/exp(exp(x^2+7*x+16)+2*log(2)),x,
algorithm="maxima")

[Out]

e^(1/8*e^(-e^(x^2 + 7*x + 16)))

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mupad [B]  time = 0.21, size = 16, normalized size = 0.70 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{-{\mathrm {e}}^{7\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{16}}}{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(- 2*log(2) - exp(7*x + x^2 + 16))/2)*exp(- 2*log(2) - exp(7*x + x^2 + 16))*exp(7*x + x^2 + 16)*(
2*x + 7))/2,x)

[Out]

exp(exp(-exp(7*x)*exp(x^2)*exp(16))/8)

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sympy [A]  time = 0.48, size = 15, normalized size = 0.65 \begin {gather*} e^{\frac {e^{- e^{x^{2} + 7 x + 16}}}{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(-2*x-7)*exp(x**2+7*x+16)*exp(1/2/exp(exp(x**2+7*x+16)+2*ln(2)))/exp(exp(x**2+7*x+16)+2*ln(2)),x
)

[Out]

exp(exp(-exp(x**2 + 7*x + 16))/8)

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