3.34.47 \(\int \frac {2 x^2+e^{e^x+x} x (-1-x-e^x x)}{x} \, dx\)

Optimal. Leaf size=19 \[ -e^{e^x+x} x+x^2+\log (3+\log (4)) \]

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Rubi [F]  time = 0.11, 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 {2 x^2+e^{e^x+x} x \left (-1-x-e^x x\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

-E^E^x + x^2 - Defer[Int][E^(E^x + x)*x, x] - Defer[Int][E^(E^x + 2*x)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 x-e^{e^x+2 x} x-e^{e^x+x} (1+x)\right ) \, dx\\ &=x^2-\int e^{e^x+2 x} x \, dx-\int e^{e^x+x} (1+x) \, dx\\ &=x^2-\int e^{e^x+2 x} x \, dx-\int \left (e^{e^x+x}+e^{e^x+x} x\right ) \, dx\\ &=x^2-\int e^{e^x+x} \, dx-\int e^{e^x+x} x \, dx-\int e^{e^x+2 x} x \, dx\\ &=x^2-\int e^{e^x+x} x \, dx-\int e^{e^x+2 x} x \, dx-\operatorname {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=-e^{e^x}+x^2-\int e^{e^x+x} x \, dx-\int e^{e^x+2 x} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 13, normalized size = 0.68 \begin {gather*} x \left (-e^{e^x+x}+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

x*(-E^(E^x + x) + x)

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fricas [A]  time = 0.62, size = 13, normalized size = 0.68 \begin {gather*} x^{2} - e^{\left (x + e^{x} + \log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 - e^(x + e^x + log(x))

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giac [A]  time = 0.26, size = 12, normalized size = 0.63 \begin {gather*} x^{2} - x e^{\left (x + e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 - x*e^(x + e^x)

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maple [A]  time = 0.05, size = 13, normalized size = 0.68

method	result	size
risch	\(x^{2}-x \,{\mathrm e}^{{\mathrm e}^{x}+x}\)	\(13\)
norman	\(x^{2}-{\mathrm e}^{x +\ln \relax (x )+{\mathrm e}^{x}}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-exp(x)*x-x-1)*exp(x+ln(x)+exp(x))+2*x^2)/x,x,method=_RETURNVERBOSE)

[Out]

x^2-x*exp(exp(x)+x)

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maxima [A]  time = 0.44, size = 20, normalized size = 1.05 \begin {gather*} x^{2} - {\left (x e^{x} - 1\right )} e^{\left (e^{x}\right )} - e^{\left (e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 - (x*e^x - 1)*e^(e^x) - e^(e^x)

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mupad [B]  time = 1.98, size = 11, normalized size = 0.58 \begin {gather*} x\,\left (x-{\mathrm {e}}^{x+{\mathrm {e}}^x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2 - exp(x + exp(x) + log(x))*(x + x*exp(x) + 1))/x,x)

[Out]

x*(x - exp(x + exp(x)))

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sympy [A]  time = 0.14, size = 10, normalized size = 0.53 \begin {gather*} x^{2} - x e^{x + e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**2 - x*exp(x + exp(x))

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