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प्रश्न
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
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उत्तर
`int ("d"x)/sqrt((2 + x)^2 - 1) = int ("d"x)/sqrt((2 + x)^2 - 1^2)`
Put 2 + x = t
dx = dt
`int ("d"x)/sqrt((2 + x)^2 - 1) = int ("d"x)/sqrt("t"^2 - 1^2)`
`int ("d"x)/sqrt(x^2 - "a"^2) = log|x + sqrt(x^2 - "a"^2)| + "c"`
= `log |"t" + sqrt("t"^2 - 1^2)| + "c"``int ("d"x)/sqrt((2 + x)^2 - 1) = log |(2 + x) + sqrt((2 + x)^2 - 1)| + "c"`
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