Evaluate the indefinite integral of csc^6(x) cot(x) using u-substitution.

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Integral of csc^6(x) cot(x)

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Find \( \int \csc^6 x \cot x \, dx \).

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What you need first

Derivatives of basic trigonometric functions
Integration by substitution (u-substitution)
Power rule for integration

What this problem tests

Tests the ability to recognize a function and its derivative within an integrand to apply u-substitution effectively.

This is a standard problem in a first-year calculus course when learning techniques of integration, specifically u-substitution with trigonometric functions.

Integral of csc^6(x) cot(x)

What you need first

What this problem tests

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