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Question
Find the integrals of the following:
`1/(25 - 4x^2)`
Solution
`int 1/(25 - 4x^2) "d"x = int 1/(4(25/4 - x^2)) "d"x`
= `1/4 int ("d"x)/((5/4)^2 - x^2)`
`int ("d"x)/("a"^2 - x^2) = 1/(2"a") log |("a" + x)/("a" - x)| + "c"`
= `1/4 xx 1/(2 xx (5/2)) log |(5/2 + x)/(5/2 - x)| + "c"`
= `1/4 xx 1/5 log |((5 + 2x)/2)/((5 - 2x)/2)| + "c"`
= `1/20 log |(5 + 2x)/(5 - 2x)| + "c"`
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