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Find the integrals of the following: 1(2+x)2-1 - Mathematics

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प्रश्न

Find the integrals of the following:

`1/sqrt((2 + x)^2 - 1)`

बेरीज
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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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पाठ 11: Integral Calculus - Exercise 11.10 [पृष्ठ २१९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 11 Integral Calculus
Exercise 11.10 | Q 3. (i) | पृष्ठ २१९

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