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Evaluate: int(x+1)e^xlog(x e^x)\ dx...

Evaluate: `int(x+1)e^xlog(x e^x)\ dx`

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To evaluate the integral \( I = \int (x + 1) e^x \log(x e^x) \, dx \), we will follow these steps: ### Step 1: Simplify the Logarithmic Expression First, we can simplify the logarithmic term: \[ \log(x e^x) = \log x + \log e^x = \log x + x \] Thus, we can rewrite the integral as: ...
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