Optimal. Leaf size=50 \[ -\text{CannotIntegrate}\left (\frac{1}{\sqrt{x+e^x}},x\right )-3 \text{CannotIntegrate}\left (\sqrt{x+e^x},x\right )+2 \sqrt{x+e^x} x+2 \sqrt{x+e^x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0810275, 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 = {} \[ \int \frac{e^x x}{\sqrt{e^x+x}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{e^x x}{\sqrt{e^x+x}} \, dx &=2 x \sqrt{e^x+x}-2 \int \sqrt{e^x+x} \, dx-\int \frac{x}{\sqrt{e^x+x}} \, dx\\ &=2 \sqrt{e^x+x}+2 x \sqrt{e^x+x}-2 \int \sqrt{e^x+x} \, dx-\int \frac{1}{\sqrt{e^x+x}} \, dx-\int \sqrt{e^x+x} \, dx\\ \end{align*}
Mathematica [A] time = 0.0970847, size = 0, normalized size = 0. \[ \int \frac{e^x x}{\sqrt{e^x+x}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.029, size = 0, normalized size = 0. \begin{align*} \int{{{\rm e}^{x}}x{\frac{1}{\sqrt{{{\rm e}^{x}}+x}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x e^{x}}{\sqrt{x + e^{x}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x e^{x}}{\sqrt{x + e^{x}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x e^{x}}{\sqrt{x + e^{x}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]