Mathematics · 2020
JEE Main · 3 September 2020, Shift 2 · Q60
If ∫ sin^-1(√(x/(1+x))) d x= A (x) tan^-1(√ x )+ B (x)+ C, where C is a constant of integration, then the ordered pair ( A (x), B (x)) can be:
If $\displaystyle \int \sin ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) \mathrm{d} x=\mathrm{A}(x) \tan ^{-1}(\sqrt{x})+$
$\displaystyle \mathrm{B}(x)+\mathrm{C}$, where C is a constant of integration, then the ordered pair $\displaystyle (\mathrm{A}(x), \mathrm{B}(x))$ can be :
Official answer
(1)
$\displaystyle (x+1,-\sqrt{x})$
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JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.