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Question
Evaluate `int 1/(4x^2 - 1) "d"x`
Solution
Let I = `int ("d"x)/(4x^2 - 1)`
= `1/4 int ("d"x)/(x^2 - 1/4)`
= `1/4 int ("d"x)/(x^2 - (1/2)^2`
= `1/4 xx 1/(2 xx 1/2) log |(x - 1/2)/(x + 1/2)| + "c"`
∴ I = `1/4 log|(2x - 1)/(2x + 1)| + "c"`
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