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Question
Evaluate:
`int dx/sqrt(5x - 4x^2)`
Evaluate
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Solution
`int dx/sqrt(5x - 4x^2)`
= `1/2 int dx/sqrt(5/4 x - x^2)`
= `1/2 int dx/sqrt(5/4 x - x^2 + (5/8)^2 - (5/8)^2`
= `1/2 int dx/sqrt((5/8)^2 - (x^2 - 5/4x + (5/8)^2)`
= `1/2 int dx/sqrt((5/8)^2 - (x - 5/8)^2)`
= `1/2 sin^-1 ((x - 5/8)/(5/8)) + c` ...`[∵ int dx/sqrt(a^2 - x^2) = sin^-1 x/a + c]`
= `1/2 sin^-1 ((8x - 5)/5) + c`
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