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Question Number 184061 by mathlove last updated on 02/Jan/23

∫((sin^(−1) (√x)−cos^(−1) (√x))/(sin^(−1) (√x)+cos^(−1) (√x)))dx=?

$$\int\frac{{sin}^{−\mathrm{1}} \sqrt{{x}}−{cos}^{−\mathrm{1}} \sqrt{{x}}}{{sin}^{−\mathrm{1}} \sqrt{{x}}+{cos}^{−\mathrm{1}} \sqrt{{x}}}{dx}=? \\ $$

Answered by SEKRET last updated on 02/Jan/23

   arcsin((√x) )+ arccos((√x) )= (𝛑/2)

$$\:\:\:\boldsymbol{\mathrm{arcsin}}\left(\sqrt{\boldsymbol{\mathrm{x}}}\:\right)+\:\boldsymbol{\mathrm{arccos}}\left(\sqrt{\boldsymbol{\mathrm{x}}}\:\right)=\:\frac{\boldsymbol{\pi}}{\mathrm{2}} \\ $$

Commented by mathlove last updated on 03/Jan/23

pleas solve it

$${pleas}\:{solve}\:{it} \\ $$

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