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

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 = 0.145014, 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., Rules used = {} \[ \int e^{x^x} x^{2 x} (1+\log (x)) \, dx \]

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]

Rubi steps

\begin{align*} \int e^{x^x} x^{2 x} (1+\log (x)) \, dx &=\int \left (e^{x^x} x^{2 x}+e^{x^x} x^{2 x} \log (x)\right ) \, dx\\ &=\int e^{x^x} x^{2 x} \, dx+\int e^{x^x} x^{2 x} \log (x) \, dx\\ &=\log (x) \int e^{x^x} x^{2 x} \, dx+\int e^{x^x} x^{2 x} \, dx-\int \frac{\int e^{x^x} x^{2 x} \, dx}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.0425892, 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 = 0.04, size = 22, normalized size = 2. \begin{align*}{{\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}}}} \end{align*}

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 = 1.14235, size = 14, normalized size = 1.27 \begin{align*}{\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(x^x - 1)*e^(x^x)

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Fricas [A]  time = 0.82625, size = 26, normalized size = 2.36 \begin{align*}{\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(x^x - 1)*e^(x^x)

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Sympy [A]  time = 0.516164, size = 8, normalized size = 0.73 \begin{align*} \left (x^{x} - 1\right ) e^{x^{x}} \end{align*}

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 [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{2 \, x}{\left (\log \left (x\right ) + 1\right )} e^{\left (x^{x}\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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