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## Homework Statement

1)∫ 6 csc^3 (x) cot x dx

## Homework Equations

## The Attempt at a Solution

6 ∫ csc^3 (x) dx) / tan x

csc^3 / tan x = csc^3 cot x

cot^2 x = csc^2 x - 1

csc^2 x = cot^2 x + 1

csc x cot x (cot^2 x + 1)

u = csc x

du = - csc x cot x dx

## Homework Statement

2)Find the length of the curve: y = ln(csc x), π/4 <= x <= π/2

## Homework Equations

## The Attempt at a Solution

L = ∫sqrt(1 + (d(ln(csc x))^2) dx from x = π/4 to π/2

d(ln(csc x)/dx = -cot x

(1 + cot x^2) = csc^2

L = ∫ csc x dx from x = π/4 to π/2