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Evaluate : (i) int(2x)/((2x+1)^(2))dx (i...

Evaluate : (i) `int(2x)/((2x+1)^(2))dx` (ii) `int((2+3x))/((3-2x))dx`

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Let's evaluate the two integrals step by step. ### (i) Evaluate \( \int \frac{2x}{(2x+1)^2} \, dx \) **Step 1: Substitution** Let \( u = 2x + 1 \). Then, differentiate to find \( du \): \[ \frac{du}{dx} = 2 \implies du = 2 \, dx \implies dx = \frac{du}{2} ...
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