3.759 \(\int \frac {x^2}{\sqrt {e^x+x}} \, dx\)

Optimal. Leaf size=16 \[ \text {Int}\left (\frac {x^2}{\sqrt {x+e^x}},x\right ) \]

[Out]

CannotIntegrate(x^2/(x+exp(x))^(1/2),x)

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Rubi [A]  time = 0.06, 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 = {} \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^2/Sqrt[E^x + x],x]

[Out]

Defer[Int][x^2/Sqrt[E^x + x], x]

Rubi steps

\begin {align*} \int \frac {x^2}{\sqrt {e^x+x}} \, dx &=\int \frac {x^2}{\sqrt {e^x+x}} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x^2/Sqrt[E^x + x],x]

[Out]

Integrate[x^2/Sqrt[E^x + x], x]

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fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\sqrt {x + e^{x}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^2/sqrt(x + e^x), x)

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maple [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\sqrt {x +{\mathrm e}^{x}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2/(x+exp(x))^(1/2),x)

[Out]

int(x^2/(x+exp(x))^(1/2),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\sqrt {x + e^{x}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^2/sqrt(x + e^x), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {x^2}{\sqrt {x+{\mathrm {e}}^x}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2/(x + exp(x))^(1/2),x)

[Out]

int(x^2/(x + exp(x))^(1/2), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\sqrt {x + e^{x}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(x**2/sqrt(x + exp(x)), x)

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