\(\int \frac {x^2}{\sqrt {e^x+x}} \, dx\) [759]

Optimal result

Integrand size = 13, antiderivative size = 13 \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx=\text {Int}\left (\frac {x^2}{\sqrt {e^x+x}},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.05 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx=\int \frac {x^2}{\sqrt {e^x+x}} \, dx \]

[In]

Int[x^2/Sqrt[E^x + x],x]

[Out]

Defer[Int][x^2/Sqrt[E^x + x], x]

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

Mathematica [N/A]

Not integrable

Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.15 \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx=\int \frac {x^2}{\sqrt {e^x+x}} \, dx \]

[In]

Integrate[x^2/Sqrt[E^x + x],x]

[Out]

Integrate[x^2/Sqrt[E^x + x], x]

Maple [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77

\[\int \frac {x^{2}}{\sqrt {{\mathrm e}^{x}+x}}d x\]

[In]

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

[Out]

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

Fricas [F(-2)]

Exception generated. \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx=\text {Exception raised: TypeError} \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx=\int \frac {x^{2}}{\sqrt {x + e^{x}}}\, dx \]

[In]

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

[Out]

Integral(x**2/sqrt(x + exp(x)), x)

Maxima [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx=\int { \frac {x^{2}}{\sqrt {x + e^{x}}} \,d x } \]

[In]

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

[Out]

integrate(x^2/sqrt(x + e^x), x)

Giac [N/A]

Not integrable

Time = 0.33 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx=\int { \frac {x^{2}}{\sqrt {x + e^{x}}} \,d x } \]

[In]

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

[Out]

integrate(x^2/sqrt(x + e^x), x)

Mupad [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \frac {x^2}{\sqrt {e^x+x}} \, dx=\int \frac {x^2}{\sqrt {x+{\mathrm {e}}^x}} \,d x \]

[In]

int(x^2/(x + exp(x))^(1/2),x)

[Out]

int(x^2/(x + exp(x))^(1/2), x)