Final answer:
To evaluate the integral ∫(5 cot&sup5; sin&sup4; d), we can rewrite the trigonometric functions using appropriate identities and then evaluate the resulting integral.
Step-by-step explanation:
To evaluate the integral ∫(5 cot&sup5; sin&sup4; d), we can use a trigonometric identity. The identity cot² θ + 1 = csc² θ can be rearranged to give cot² θ = csc² θ - 1. Using this identity, we can rewrite cot&sup5; as (csc² - 1)² csc⊃2;, and sin&sup4; as (1 - cos⊃2;)². Substituting these expressions into the integral, we get: ∫ 5(csc² - 1)² csc&sup4; d.