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Question
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
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Solution
I = `int (1)/(25 - 9x^2)*dx`
= `int(1)/(5^2 - (3x)^2)*dx`
= `(1)/(2(5))log |(5 + 3x)/(5 - 3x)|*(1)/(3) + c`
= `(1)/(30)log |(5 + 3x)/(5 - 3x)| + c`
Alternative Method:
`int (1)/(25 - 9x^2)*dx`
= `(1)/(9) int (1)/((25)/(9)x^2)*dx`
= `(1)/(9) int (1)/((5/3)^2 - x^2)*dx`
= `(1)/(9) xx (1)/(2 xx 5/3)log|(5/3 + x)/(5 / 3 - x)|+ c`
= `(1)/(30)log|(5 + 3x)/(5 - 3x)| + c`
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