Evaluating \(\displaystyle{\int_{{0}}^{{\sqrt{{{3}}}}}}{\arcsin{{\left({\frac{{{2}{t}}}{{{1}+{t}^{{2}}}}}\right)}}}{\left.{d}{t}\right.}\)

Beryneingmk39 2022-04-05 Answered
Evaluating 03arcsin(2t1+t2)dt
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Answers (1)

Jambrichp2w2
Answered 2022-04-06 Author has 12 answers
We have
ddtarcsin(2t1+t2)=114t2(1+t2)2(2t1+t2)
=(1+t2)(1+t2)24t2(2(1+t2)4t2(1+t2)2)
=(1+t2)(1t2)2(2(1t2)(1+t2)2)
=2(1t2)(1+t2)(t21)2
=2(1t2)(1+t2)|t21|
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