Evaluate: (i) `int(sin2x)/(sin5xsin3x)\ dx` (ii) `int(1+cotx)/(x+logsinx)\ dx`

Explanation

(i)

`int frac{sin 2 x}{sin 5 x sin 3 x} d x `

`=int frac{sin (5 x-3 x)}{sin 5 x sin 3 x} d x `

`=int frac{sin 5 x cos 3 x-cos 5 x sin 3 x}{sin 5 x sin 3 x} d x `

`=int frac{sin 5 x cos 3 x}{sin 5 x sin 3 x}-frac{cos 5 x sin 3 x}{sin 5 x sin 3 x} d x `

`=int[cot 3 x-cot 5 x] d x `

`=int cot 3 x d x-int cot 5 x d x `

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