integration

\int \frac{dx}{(1+\sqrt{x})\sqrt{x-x^{2}}} is equal to ?

please give a proper method along with your answer.

1 Answers

take a âˆšx out of the âˆš(x-x²), to make it âˆšxâˆš(1-x)*(1+âˆšx)

put âˆšx =t and then t=sinA to get

2âˆ«dA/(1+sinA)

=2âˆ«(1-sinA)/cos²A

=2âˆ«sec²AdA -2âˆ«secAtanAdA

=2[tanA-secA]

cheers!!

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