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Question
Integrate the function `1/sqrt(9 - 25x^2)`
Solution
Let `I = int dx/sqrt(9 - 25 x^2)`
`= 1/5 int dx/ (sqrt (9/25 - x^2))`
`= 1/5 int dx/ sqrt ((3/5)^2 - x^2)`
`1/5 sin^-1 (x /(3/5)) + C` ....`[∵ int dx/sqrt (a^2 - x^2) = sin^-1 x/a + C]`
`= 1/5 sin^-1 ((5x)/3) + C`
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