3.89.39 \(\int \frac {e^{-\frac {e^x (-14-7 x)-2 x}{x}+x} (-14+14 x+7 x^2)}{x^2} \, dx\)

Optimal. Leaf size=20 \[ e^{-x+\left (1+\frac {7 e^x}{x}\right ) (2+x)} \]

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Rubi [F]  time = 0.78, 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 {e^{-\frac {e^x (-14-7 x)-2 x}{x}+x} \left (-14+14 x+7 x^2\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-((E^x*(-14 - 7*x) - 2*x)/x) + x)*(-14 + 14*x + 7*x^2))/x^2,x]

[Out]

7*Defer[Int][E^(((2 + x)*(7*E^x + x))/x), x] - 14*Defer[Int][E^(((2 + x)*(7*E^x + x))/x)/x^2, x] + 14*Defer[In
t][E^(((2 + x)*(7*E^x + x))/x)/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {(2+x) \left (7 e^x+x\right )}{x}} \left (-14+14 x+7 x^2\right )}{x^2} \, dx\\ &=\int \left (7 e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}-\frac {14 e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}}{x^2}+\frac {14 e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}}{x}\right ) \, dx\\ &=7 \int e^{\frac {(2+x) \left (7 e^x+x\right )}{x}} \, dx-14 \int \frac {e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}}{x^2} \, dx+14 \int \frac {e^{\frac {(2+x) \left (7 e^x+x\right )}{x}}}{x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.13, size = 15, normalized size = 0.75 \begin {gather*} e^{2+\frac {7 e^x (2+x)}{x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-((E^x*(-14 - 7*x) - 2*x)/x) + x)*(-14 + 14*x + 7*x^2))/x^2,x]

[Out]

E^(2 + (7*E^x*(2 + x))/x)

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fricas [A]  time = 0.51, size = 23, normalized size = 1.15 \begin {gather*} e^{\left (-x + \frac {x^{2} + 7 \, {\left (x + 2\right )} e^{x} + 2 \, x}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((7*x^2+14*x-14)*exp(x)/x^2/exp(((-7*x-14)*exp(x)-2*x)/x),x, algorithm="fricas")

[Out]

e^(-x + (x^2 + 7*(x + 2)*e^x + 2*x)/x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((7*x^2+14*x-14)*exp(x)/x^2/exp(((-7*x-14)*exp(x)-2*x)/x),x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.07, size = 19, normalized size = 0.95

method	result	size
risch	\({\mathrm e}^{\frac {7 \,{\mathrm e}^{x} x +14 \,{\mathrm e}^{x}+2 x}{x}}\)	\(19\)
norman	\({\mathrm e}^{-\frac {\left (-7 x -14\right ) {\mathrm e}^{x}-2 x}{x}}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((7*x^2+14*x-14)*exp(x)/x^2/exp(((-7*x-14)*exp(x)-2*x)/x),x,method=_RETURNVERBOSE)

[Out]

exp((7*exp(x)*x+14*exp(x)+2*x)/x)

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maxima [A]  time = 0.45, size = 14, normalized size = 0.70 \begin {gather*} e^{\left (\frac {14 \, e^{x}}{x} + 7 \, e^{x} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((7*x^2+14*x-14)*exp(x)/x^2/exp(((-7*x-14)*exp(x)-2*x)/x),x, algorithm="maxima")

[Out]

e^(14*e^x/x + 7*e^x + 2)

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mupad [B]  time = 5.21, size = 16, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^2\,{\mathrm {e}}^{\frac {14\,{\mathrm {e}}^x}{x}}\,{\mathrm {e}}^{7\,{\mathrm {e}}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((2*x + exp(x)*(7*x + 14))/x)*exp(x)*(14*x + 7*x^2 - 14))/x^2,x)

[Out]

exp(2)*exp((14*exp(x))/x)*exp(7*exp(x))

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sympy [A]  time = 0.19, size = 17, normalized size = 0.85 \begin {gather*} e^{- \frac {- 2 x + \left (- 7 x - 14\right ) e^{x}}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((7*x**2+14*x-14)*exp(x)/x**2/exp(((-7*x-14)*exp(x)-2*x)/x),x)

[Out]

exp(-(-2*x + (-7*x - 14)*exp(x))/x)

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