Integral of $$$\left(\frac{x}{2}\right)^{x} \left(\frac{2}{x}\right)^{x}$$$

The calculator will find the integral/antiderivative of $$$\left(\frac{x}{2}\right)^{x} \left(\frac{2}{x}\right)^{x}$$$, with steps shown.

Find $$$\int \left(\frac{x}{2}\right)^{x} \left(\frac{2}{x}\right)^{x}\, dx$$$.

The input is rewritten: $$$\int{\left(\frac{x}{2}\right)^{x} \left(\frac{2}{x}\right)^{x} d x}=\int{1 d x}$$$.

Apply the constant rule $$$\int c\, dx = c x$$$ with $$$c=1$$$:

$${\color{red}{\int{1 d x}}} = {\color{red}{x}}$$

Therefore,

$$\int{1 d x} = x$$

Add the constant of integration:

$$\int{1 d x} = x+C$$

$$$\int \left(\frac{x}{2}\right)^{x} \left(\frac{2}{x}\right)^{x}\, dx = x + C$$$A

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