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MathPhys

Step-by-step explanation:

12 ∫ (cot⁴(3x) csc²(3x)) dx

If u = cot(3x), then du = -3 csc²(3x) dx.  So -⅓ du = csc²(3x) dx.

12 ∫ u⁴ (-⅓ du)

-4 ∫ u⁴ du

-⅘ u⁵ + C

Substituting back:

-⅘ cot⁵(3x) + C

Evaluate between x=0 and x=π/12.  cot(0) is undefined, so the integral does not exist.

lillyfyobrien

Answer:

12 ∫ (cot⁴(3x) csc²(3x)) dx

If u = cot(3x), then du = -3 csc²(3x) dx.  So -⅓ du = csc²(3x) dx.

12 ∫ u⁴ (-⅓ du)

-4 ∫ u⁴ du

-⅘ u⁵ + C

Substituting back:

-⅘ cot⁵(3x) + C

Evaluate between x=0 and x=π/12.  cot(0) is undefined, so the integral does not exist.

Step-by-step explanation:

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