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... 1(x)cot(x)+(2k−1)∫csc2k−1(x)dx]. Proof: ∫csc2k+1(x)dx=∫csc2k−1(x)csc2(x)dx. Using integration by parts: Let u=csc2k−1(x). then du=−(2k−1)csc2k−1(x)cot(x)dx. Jan 10, 2024 ... ... - y) = (cot x + cot y)/(1 + cot x cot y). Verified step by step guidance. 1. Step 1: Start by expressing and in terms of sine and cosine: and . Jan 27, 2020 ... = 2n. Z sec2n+1 xdx-. Z sec2n-1 xdx-. Z sec2n-3 xdx-...-. Z secxdx,. C2n-1 -cscx+cotx sec2n-1 x = = 2(n-1). Z sec2n-1 xdx-. Z sec2n-3 xdx-. Jan 28, 2016 ... csc x cot x dx = − csc x+C. ∫ sec x tan x dx = sec x+C = ∫ csc2 x ... 1. Evaluate the following integrals. (a) (3 points). ∫ x + 3. Detailed step by step solution for csc^2(x)=cot(x)+1. Feb 5, 2025 ... Concepts: Trigonometry, Cotangent function. Explanation: To solve the equation cot(x)=1, we need to find the values of x for which the ... ... 1) and having the interval between x, and x+1 as base, i.e., let. It follows from (1) that. (2) h₁ = xnxn+1/(coty-cotx). }ĥ

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