∫ e 1 ___27 (−600+25e2+2x+ex(1+x) ____________________x )+2+2x+ex(1+x) x (−50+ex(−25+25x+25x2)) _____________________________________________________________________________________________

Optimal. Leaf size=26 \[ e^{\frac {25}{9} \left (-8+\frac {1}{3} e^{\frac {\left (2+e^x\right ) (1+x)}{x}}\right )} \]

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Rubi [F] time = 6.32, 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 (\frac {1}{27} \left (-600+25 e^{\frac {2+2 x+e^x (1+x)}{x}}\right )+\frac {2+2 x+e^x (1+x)}{x}\right ) \left (-50+e^x \left (-25+25 x+25 x^2\right )\right )}{27 x^2} \, dx \end {gather*}

Int[(E^((-600 + 25*E^((2 + 2*x + E^x*(1 + x))/x))/27 + (2 + 2*x + E^x*(1 + x))/x)*(-50 + E^x*(-25 + 25*x + 25*

(25*Defer[Int][E^(x + (54 + 27*E^x - 546*x + 27*E^x*x + 25*E^(((2 + E^x)*(1 + x))/x)*x)/(27*x)), x])/27 - (50*

Defer[Int][E^((54 + 27*E^x - 546*x + 27*E^x*x + 25*E^(((2 + E^x)*(1 + x))/x)*x)/(27*x))/x^2, x])/27 - (25*Defe

r[Int][E^(x + (54 + 27*E^x - 546*x + 27*E^x*x + 25*E^(((2 + E^x)*(1 + x))/x)*x)/(27*x))/x^2, x])/27 + (25*Defe

r[Int][E^(x + (54 + 27*E^x - 546*x + 27*E^x*x + 25*E^(((2 + E^x)*(1 + x))/x)*x)/(27*x))/x, x])/27

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{27} \int \frac {\exp \left (\frac {1}{27} \left (-600+25 e^{\frac {2+2 x+e^x (1+x)}{x}}\right )+\frac {2+2 x+e^x (1+x)}{x}\right ) \left (-50+e^x \left (-25+25 x+25 x^2\right )\right )}{x^2} \, dx\\ &=\frac {1}{27} \int \frac {\exp \left (\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right ) \left (-50+e^x \left (-25+25 x+25 x^2\right )\right )}{x^2} \, dx\\ &=\frac {1}{27} \int \left (-\frac {50 \exp \left (\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )}{x^2}+\frac {25 \exp \left (x+\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right ) \left (-1+x+x^2\right )}{x^2}\right ) \, dx\\ &=\frac {25}{27} \int \frac {\exp \left (x+\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right ) \left (-1+x+x^2\right )}{x^2} \, dx-\frac {50}{27} \int \frac {\exp \left (\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )}{x^2} \, dx\\ &=\frac {25}{27} \int \left (\exp \left (x+\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )-\frac {\exp \left (x+\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )}{x^2}+\frac {\exp \left (x+\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )}{x}\right ) \, dx-\frac {50}{27} \int \frac {\exp \left (\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )}{x^2} \, dx\\ &=\frac {25}{27} \int \exp \left (x+\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right ) \, dx-\frac {25}{27} \int \frac {\exp \left (x+\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )}{x^2} \, dx+\frac {25}{27} \int \frac {\exp \left (x+\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )}{x} \, dx-\frac {50}{27} \int \frac {\exp \left (\frac {54+27 e^x-546 x+27 e^x x+25 e^{\frac {\left (2+e^x\right ) (1+x)}{x}} x}{27 x}\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 1.99, size = 22, normalized size = 0.85 \begin {gather*} e^{\frac {25}{27} \left (-24+e^{\frac {\left (2+e^x\right ) (1+x)}{x}}\right )} \end {gather*}

Integrate[(E^((-600 + 25*E^((2 + 2*x + E^x*(1 + x))/x))/27 + (2 + 2*x + E^x*(1 + x))/x)*(-50 + E^x*(-25 + 25*x

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fricas [B] time = 0.68, size = 54, normalized size = 2.08 \begin {gather*} e^{\left (\frac {27 \, {\left (x + 1\right )} e^{x} + 25 \, x e^{\left (\frac {{\left (x + 1\right )} e^{x} + 2 \, x + 2}{x}\right )} - 546 \, x + 54}{27 \, x} - \frac {{\left (x + 1\right )} e^{x} + 2 \, x + 2}{x}\right )} \end {gather*}

integrate(1/27*((25*x^2+25*x-25)*exp(x)-50)*exp(((x+1)*exp(x)+2*x+2)/x)*exp(25/27*exp(((x+1)*exp(x)+2*x+2)/x)-

e^(1/27*(27*(x + 1)*e^x + 25*x*e^(((x + 1)*e^x + 2*x + 2)/x) - 546*x + 54)/x - ((x + 1)*e^x + 2*x + 2)/x)

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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {25 \, {\left ({\left (x^{2} + x - 1\right )} e^{x} - 2\right )} e^{\left (\frac {{\left (x + 1\right )} e^{x} + 2 \, x + 2}{x} + \frac {25}{27} \, e^{\left (\frac {{\left (x + 1\right )} e^{x} + 2 \, x + 2}{x}\right )} - \frac {200}{9}\right )}}{27 \, x^{2}}\,{d x} \end {gather*}

integrate(1/27*((25*x^2+25*x-25)*exp(x)-50)*exp(((x+1)*exp(x)+2*x+2)/x)*exp(25/27*exp(((x+1)*exp(x)+2*x+2)/x)-

integrate(25/27*((x^2 + x - 1)*e^x - 2)*e^(((x + 1)*e^x + 2*x + 2)/x + 25/27*e^(((x + 1)*e^x + 2*x + 2)/x) - 2

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method	result	size

risch	\({\mathrm e}^{\frac {25 \,{\mathrm e}^{\frac {\left ({\mathrm e}^{x}+2\right ) \left (x +1\right )}{x}}}{27}-\frac {200}{9}}\)	\(18\)
norman	\({\mathrm e}^{\frac {25 \,{\mathrm e}^{\frac {\left (x +1\right ) {\mathrm e}^{x}+2 x +2}{x}}}{27}-\frac {200}{9}}\)	\(22\)

int(1/27*((25*x^2+25*x-25)*exp(x)-50)*exp(((x+1)*exp(x)+2*x+2)/x)*exp(25/27*exp(((x+1)*exp(x)+2*x+2)/x)-200/9)

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maxima [A] time = 0.47, size = 21, normalized size = 0.81 \begin {gather*} e^{\left (\frac {25}{27} \, e^{\left (\frac {e^{x}}{x} + \frac {2}{x} + e^{x} + 2\right )} - \frac {200}{9}\right )} \end {gather*}

integrate(1/27*((25*x^2+25*x-25)*exp(x)-50)*exp(((x+1)*exp(x)+2*x+2)/x)*exp(25/27*exp(((x+1)*exp(x)+2*x+2)/x)-

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mupad [B] time = 5.43, size = 24, normalized size = 0.92 \begin {gather*} {\mathrm {e}}^{-\frac {200}{9}}\,{\mathrm {e}}^{\frac {25\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,{\mathrm {e}}^{2/x}}{27}} \end {gather*}

int((exp((25*exp((2*x + exp(x)*(x + 1) + 2)/x))/27 - 200/9)*exp((2*x + exp(x)*(x + 1) + 2)/x)*(exp(x)*(25*x +

exp(-200/9)*exp((25*exp(exp(x))*exp(2)*exp(exp(x)/x)*exp(2/x))/27)

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sympy [A] time = 0.92, size = 22, normalized size = 0.85 \begin {gather*} e^{\frac {25 e^{\frac {2 x + \left (x + 1\right ) e^{x} + 2}{x}}}{27} - \frac {200}{9}} \end {gather*}

integrate(1/27*((25*x**2+25*x-25)*exp(x)-50)*exp(((x+1)*exp(x)+2*x+2)/x)*exp(25/27*exp(((x+1)*exp(x)+2*x+2)/x)

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3.78.6 \(\int \frac {e^{\frac {1}{27} (-600+25 e^{\frac {2+2 x+e^x (1+x)}{x}})+\frac {2+2 x+e^x (1+x)}{x}} (-50+e^x (-25+25 x+25 x^2))}{27 x^2} \, dx\)