Integrate with respect to x: i) `sin^(2)x`, ii) `cos^(3)x` , iii) `sin2xcos3x`, iv) `1/(sqrt(x+3)-sqrt(x+2))`

Explanation

Let's solve the given integrals step by step.

### i) Integrate \( \sin^2 x \)

To integrate \( \sin^2 x \), we can use the identity:
\[ \sin^2 x = \frac{1 - \cos(2x)}{2} \]
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