3.7.92 \(\int e^{x^x} x^{2 x} (1+\log (x)) \, dx\) [692]

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

[Out]

exp(x^x)*(-1+x^x)

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Rubi [F]
time = 0.10, 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 e^{x^x} x^{2 x} (1+\log (x)) \, dx \end {gather*}

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*}

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Mathematica [A]
time = 0.02, size = 11, normalized size = 1.00 \begin {gather*} e^{x^x} \left (-1+x^x\right ) \end {gather*}

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 [A]
time = 0.02, size = 11, normalized size = 1.00

method	result	size
risch	\({\mathrm e}^{x^{x}} \left (-1+x^{x}\right )\)	\(11\)
norman	\({\mathrm e}^{\ln \left (x \right ) x} {\mathrm e}^{{\mathrm e}^{\ln \left (x \right ) x}}-{\mathrm e}^{{\mathrm e}^{\ln \left (x \right ) x}}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x^x)*(-1+x^x)

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Maxima [A]
time = 0.36, size = 10, normalized size = 0.91 \begin {gather*} {\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \end {gather*}

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 = 0.37, size = 10, normalized size = 0.91 \begin {gather*} {\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \end {gather*}

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 = 0.15, size = 8, normalized size = 0.73 \begin {gather*} \left (x^{x} - 1\right ) e^{x^{x}} \end {gather*}

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 [A]
time = 5.53, size = 10, normalized size = 0.91 \begin {gather*} {\left (x^{x} - 1\right )} e^{\left (x^{x}\right )} \end {gather*}

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]

(x^x - 1)*e^(x^x)

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Mupad [B]
time = 3.59, size = 10, normalized size = 0.91 \begin {gather*} {\mathrm {e}}^{x^x}\,\left (x^x-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(2*x)*exp(x^x)*(log(x) + 1),x)

[Out]

exp(x^x)*(x^x - 1)

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