JavaScript is disabled. For a far better experience, please allow JavaScript in your browser prior to proceeding.

You are watching: Sin−1(x) dx

This is a solution to the question, which I discovered on the web. The just bit I"m not certain of, is the transition from the 3rd last line to second last line (highlighted in bold). I would certainly have fixed ?(1/2)u^(-1/2) du as -1/2 (sin^(-1)x), but I"m assuming that when du is characterized, integration is ignored and we simply extract the (displaystyle sqrtu). Can anyone aid clarify this with me?Many kind of thanks.Q. Integprice sin^(-1) x dxAns.: combine by partslet u = arcsinx ; dv = dxdu = dx/?(1-x²) ; v = xx arcsinx - ?x/?(1-x²) dxlet u = 1-x²du = -2x dxx dx = (-1/2)dux arcsinx - ?(-1/2)du / ?(u)x arcsinx + ?(1/2)u^(-1/2) dux arcsinx + u^(1/2)x arcsinx + ?(1-x²) + C
I changed the answer a little bit for you. I think currently you will understand also let u = arcsinx ; dv = dxdu = dx/?(1-x²) ; v = xx arcsinx - ?x/?(1-x²) dxlet t = 1-x²dt = -2x dxx dx = (-1/2)dtx arcsinx - ?(-1/2)dt / ?(t)x arcsinx + ?(1/2)t^(-1/2) dtx arcsinx + t^(1/2)x arcsinx + ?(1-x²) + C
Apologies, yet I"m not seeing much distinction from the answer gave and what you"re showing right here, i.e. respecifying "let u = 1-x²" with "let t = 1-x²"? My question still stands. What is occuring in between "x arcsinx + ?(1/2)u^(-1/2) du" & "x arcsinx + u^(1/2)"? What integration has actually taken place?

(displaystyle xarcsin(x),+,frac12int u^-1/2,du,=,xarcsin(x),+,frac12,cdot,fracu^-frac12,+,1-frac12,+,1,+,C,=,xarcsin(x),+,u^frac12,+,C)
Similar Math DiscussionsMath ForumDate
Integrate From 0 to InfinityCalculusJan 6, 2021
combine From 0 to 1CalculusJan 6, 2021
How to integrateCalculusOct 9, 2020
incorporate sin^-1(cosx)+cos^-1(sinx) dxCalculusApr 3, 2014

Similar threads
Integprice From 0 to Infinity
incorporate From 0 to 1
How to integrate
incorporate sin^-1(cosx)+cos^-1(sinx) dx

See more: Grand Army Of The Republic Apush, Woodrow Wilson: Foreign Affairs

Math Forums

Math Forums gives a cost-free community for students, teachers, educators, professors, mathematicians, designers, researchers, and also hobbyists to learn and talk about mathematics and also scientific research. Our primary emphasis is math discussions and free math help; science discussions around physics, chemistry, computer science; and also academic/career guidance. Our area is totally free to join and also participate, and we welcome everyone from about the people to talk about math and science at all levels.