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प्रश्न
`int 1/(4x^2 - 1) dx` = ______.
उत्तर
`int 1/(4x^2 - 1) dx = bb(underline(1/4log |(2x - 1)/(2x + 1)|)`.
Explanation:
`int 1/(4x^2 - 1) dx = int 1/(4(x^2 - 1/4))dx`
= `1/4 int 1/(x^2 - (1/2)^2)dx`
= `1/4 log|(x - 1/2)/(x + 1/2)|`
= `1/4 log|(2x - 1)/(2x + 1)|`
∴ `int 1/(4x^2 - 1) dx = 1/4 log|(2x - 1)/(2x + 1)|`
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