3.675 \(\int e^{x^x} x^{2 x} (1+\log (x)) \, dx\)

Optimal. Leaf size=11 \[ e^{x^x} \left (x^x-1\right ) \]

[Out]

E^x^x*(-1 + x^x)

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Rubi [F]  time = 0.212078, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (e^{x^x} x^{2 x} (1+\log (x)),x\right ) \]

Verification is Not applicable to the result.

[In]  Int[E^x^x*x^(2*x)*(1 + Log[x]),x]

[Out]

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

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int x^{2 x} \left (\log{\left (x \right )} + 1\right ) e^{x^{x}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x**x)*x**(2*x)*(1+ln(x)),x)

[Out]

Integral(x**(2*x)*(log(x) + 1)*exp(x**x), x)

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Mathematica [A]  time = 0.0110554, size = 11, normalized size = 1. \[ e^{x^x} \left (x^x-1\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[E^x^x*x^(2*x)*(1 + Log[x]),x]

[Out]

E^x^x*(-1 + x^x)

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Maple [B]  time = 0.027, size = 22, normalized size = 2. \[{{\rm e}^{\ln \left ( x \right ) x}}{{\rm e}^{{{\rm e}^{\ln \left ( x \right ) x}}}}-{{\rm e}^{{{\rm e}^{\ln \left ( x \right ) x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x^x)*x^(2*x)*(1+ln(x)),x)

[Out]

exp(ln(x)*x)*exp(exp(ln(x)*x))-exp(exp(ln(x)*x))

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Maxima [A]  time = 0.915001, size = 14, normalized size = 1.27 \[{\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(2*x)*(log(x) + 1)*e^(x^x),x, algorithm="maxima")

[Out]

(x^x - 1)*e^(x^x)

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Fricas [A]  time = 0.247699, size = 14, normalized size = 1.27 \[{\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(2*x)*(log(x) + 1)*e^(x^x),x, algorithm="fricas")

[Out]

(x^x - 1)*e^(x^x)

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Sympy [A]  time = 0.822321, size = 8, normalized size = 0.73 \[ \left (x^{x} - 1\right ) e^{x^{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x**x)*x**(2*x)*(1+ln(x)),x)

[Out]

(x**x - 1)*exp(x**x)

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int x^{2 \, x}{\left (\log \left (x\right ) + 1\right )} e^{\left (x^{x}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(2*x)*(log(x) + 1)*e^(x^x),x, algorithm="giac")

[Out]

integrate(x^(2*x)*(log(x) + 1)*e^(x^x), x)