Integrate \int_0^1 \sin^{-1}{\frac{x^2}{1+x^2}}dx

Turnseeuw

Turnseeuw

Answered question

2022-01-30

Integrate 01sin1{x21+x2}dx

Answer & Explanation

egowaffle26ic

egowaffle26ic

Beginner2022-01-31Added 7 answers

01arcsin(x21+x2),dx=01arcsin(x1+x)dx2x
equals
012arcsin(u)2u12(1u)32du
which can be managed by integration by parts. It boils down to
π6012u1udu1u2du
then to
π6+log(2+3)2log(2+3)0.219563

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