Questions: ∫ sqrt((2x+1)/(x+2)) dx

Transcript text: $\int \sqrt{\frac{2 x+1}{x+2}} d x$

Solution

Solution Steps

Step 1: Define the Integral

We start with the integral we want to solve: \[ I = \int \sqrt{\frac{2x + 1}{x + 2}} \, dx \]

Step 2: Set Up the Integral

The integrand is given by: \[ \text{integrand} = \sqrt{\frac{2x + 1}{x + 2}} \] We will integrate this expression with respect to $x$.

Step 3: Perform the Integration

The integral can be expressed as: \[ I = \int \sqrt{\frac{2x + 1}{x + 2}} \, dx \] This integral does not have a simple antiderivative in terms of elementary functions, and thus we leave it in its integral form.

Final Answer

The integral is expressed as: \[ \boxed{I = \int \sqrt{\frac{2x + 1}{x + 2}} \, dx} \]

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