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Question
Evaluate the integral by using substitution.
`int_(-1)^1 dx/(x^2 + 2x + 5)`
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Solution
`int_-1^1 dx/(x^2 + 2x + 5)`
`= int_-1^1 dx/(x^2 + 2x + 4 + 1)`
`int_-1^1 dx/((x + 2)^2 + (1)^2)`
`= 1/2 [tan^-1 ((x + 1)/2)]_-1^1`
`= 1/2 [tan^-1 (1) - tan^-1 0]`
`= 1/2 [pi/4 - 0]`
`= pi/8`
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