Evaluate the following integrals :
`(i) int sin^(4)xcos^(2)xdx` `(ii) intsec^((4)/(9))x cosec^((14)/(9))xdx`

Explanation

Let's evaluate the given integrals step by step.

### (i) Evaluate the integral \( \int \sin^4 x \cos^2 x \, dx \)

1. **Rewrite the integral**: We can express \( \sin^4 x \) as \( \sin^2 x \cdot \sin^2 x \) and use the identity \( \sin^2 x = 1 - \cos^2 x \).
\[ \int \sin^4 x \cos^2 x \, dx = \int (\sin^2 x)^2 \cos^2 x \, dx = \int (1 - \cos^2 x)^2 \cos^2 x \, dx \]
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