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Question
Integrate the following with respect to x:
`8/sqrt(1 - (4x)^2) + 27/sqrt(1 - 9x^2) - 15/(1 + 25x^2)`
Solution
`int [8/sqrt(1 - (4x)^2) + 27/sqrt(1 - 9x^2) - 15/(1 + 25x^2)] "d"x`
= `8 int 1/sqrt(1 - (4x)^2) "d"x + 24int 1/sqrt(1 - (3x)^2) "d"x - 15int 1/sqrt(1 + (5x)^2) "d"x`
= `8/4 sin^-1 (4x) + 27/3 sin^-1 (3x) (- 15)/5 tan^-1 (5x) + "c"`
= `2sin^-1 (4x) + 9sin^-1 (3x) - 3tan^-1(5x) + "c"`
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