Evaluate:`int1/xsqrt((1-sqrt(x))/(1+sqrt(x))dx)`

1.	Evaluate:`int1/xsqrt((1-sqrt(x))/(1+sqrt(x))dx)`
Answer» Put ` x= cos^(2)theta` `impliesdx= -2cos theta sin theta d theta` ` :. I=int(1)/(x)sqrt((1-sqrt(x))/(1+sqrt(x)))dx` `=intsqrt((1-cos theta)/(1+cos theta))* (-2cos theta sin theta)/(cos^(2) theta) d theta` `= -int ("sin"(theta)/(2))/("cos"(theta)/(2))*(4"sin"(theta)/(2)"cos"(theta)/(2))/("cos"theta)d theta ` `= -2 int (2 "sin"^(2)(theta)/(2))/(cos theta) d theta` `= -2int(1-cos theta)/(cos theta)d theta` `= -2 int (sec theta -1)d theta` `= - 2 [log_(e)\|sec theta+tan theta\|-theta] +c` `= -2[log_(e)\|(1)/(sqrt(x))+(sqrt(1-x))/(sqrt(x))\|-"cos"^(-1)sqrt(x)]+c` `= -2[log_(e)\|(1+sqrt(1-x))/(sqrt(x))\|-cos^(-1)sqrt(x)] +c`

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Evaluate:`int1/xsqrt((1-sqrt(x))/(1+sqrt(x))dx)`

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