Evaluate:`intsin^(-1)sqrt(x/(a+x))dxdot`

1.	Evaluate:`intsin^(-1)sqrt(x/(a+x))dxdot`
Answer» `I=int sin^(-1)sqrt((x)/(a+x))dx` Let `x=a tan^(2) theta " or " dx=2a tan theta sec^(2)theta d theta` `:. intsin^(-1)sqrt(sin^(2)theta)2a sec^(2)theta tan theta d theta` `=2a int underset(I)(underbrace(theta)) underset(II)(underbrace(sec^(2) theta tan theta)) d theta` `=2a[theta(tan^(2)theta)/(2)-int(tan^(2)theta)/(2) d theta]` `=a[ theta tan^(2)theta-int(sec^(2) theta-1) d theta]` `=a(theta tan^(2) theta-tan theta + theta]+c, " where " theta ="tan"^(-1)sqrt((x)/(a))`

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Evaluate:`intsin^(-1)sqrt(x/(a+x))dxdot`

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