Can you indefinite the integral of x^2.arcsin(x) please?

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Answered question

2021-08-22

Can you indefinite the integral of x2arcsin(x) please?

Answer & Explanation

wheezym

wheezym

Skilled2021-08-23Added 103 answers

indefinite integral of x2.arcsin(x), using integration by parts.
we use the fact that asin(x)=x.asin(x)+(1x2)12
x2.arcsin(x)dx=x2{x.asin(x)+(1x2)12}{2x.x.asin(x)+2x.(1x2)12dx}
x2.arcsin(x)dx=x2{x.asin(x)+(1x2)12}2{x2.asin(x)dx}{2x.(1x2)12dx}
3{x2.arcsin(x)dx}=x2{x.asin(x)+(1x2)12}{2x.(1x2)12dx}
3{x2.arcsin(x)dx}=x2{x.asin(x)+(1x2)12}{(23)(1x2)32}
3{x2.arcsin(x)dx}=x2.x.asin(x)+x2.(1x2)12

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