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Evaluate int(dx)/(1-x-x^(2))...

Evaluate `int(dx)/(1-x-x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
` -(1)/(sqrt(5))log_(e)|(2x+1-sqrt(5))/(2x+1+sqrt(5))|+C`
`I= -int(dx)/(x^(2)+x-1)= -int(dx)/((x+(1)/(2))^(2)-(5)/(4))`
`=-(1)/(2*(sqrt(5))/(2))"log"_(e)|((x+(1)/(2))-(sqrt(5))/(2))/((x+(1)/(2))+(sqrt(5))/(2))|+C`
`= -(1)/(sqrt(5))log_(e)|(2x+1-sqrt(5))/(2x+1+sqrt(5))|+C`
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