Nettet2. nov. 2015 · ∫(cscx)2dx = − cotx + C Explanation: The derivative of cotx is csc2x, so the integral of csc2x is cotx + C If you really want the integral of the integral, then use: ∫[∫(cscx)2dx]dx = ∫[ − cotx + C]dx where C is an arbitrary constant = ∫( − cosx sinx + C)dx where C is an arbitrary constant = − ln sinx +Cx + D where C,D are arbitrary constants NettetEvaluate the Integral integral of (csc (x)-tan (x))^2 with respect to x ∫ (csc(x) − tan(x))2dx ∫ ( csc ( x) - tan ( x)) 2 d x Simplify. Tap for more steps... ∫ csc2(x)− 2sec(x)+tan2 (x)dx …
Integral of Cosecant Cubed X eMathZone
NettetTour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site NettetSet up the integral to solve. F (x) = ∫ csc2 (x)dx F ( x) = ∫ csc 2 ( x) d x Since the derivative of −cot(x) - cot ( x) is csc2 (x) csc 2 ( x), the integral of csc2(x) csc 2 ( x) is −cot(x) - cot ( x). −cot(x)+ C - cot ( x) + C The answer is the antiderivative of the function f (x) = csc2(x) f ( x) = csc 2 ( x). lhd headlights
3.5: Derivatives of Trigonometric Functions - Mathematics LibreTexts
NettetProof: Integral csc (x) ( Math Calculus Integrals Table Of csc x) Discussion of csc x = - ln csc x + cot x + C. 1. Proof Strategy: The strategy is not obvious. Multiply and … Nettet18. feb. 2024 · Explanation: There are many ways to prove this result. The quickest method that I am aware of is as follows: ∫ cscx dx = ∫ cscx cscx +cotx cscx +cotx dx. = ∫ csc2x +cscxcotx cscx +cotx dx. Then we perform simple substitution, Let. u = cscx +cotx ⇒ du dx = −cscxcotx − csc2x. = − (cscxcotx +csc2x) And so: NettetThe integral of the cosecant cubed of X is of the form I = ∫ csc 3 x d x – – – ( i) First we break csc 3 x into csc x and csc 2 x, and now the integral (i) becomes I = ∫ csc x csc 2 x d x – – – ( ii) csc x and csc 2 x are the first and second functions that form integration by parts. Using the formula for integration by parts, we have mcdowell medsource