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

Find the integrals of the following:

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

बेरीज

`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]

पाठ 11 Integral Calculus
Exercise 11.10 | Q 3. (i) | पृष्ठ २१९

Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`

Integrate the following functions with respect to x :

`(sin4x)/sinx`

Integrate the following functions with respect to x :

`(x + 1)/((x + 2)(x + 3))`

Integrate the following with respect to x :

`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`

Integrate the following with respect to x :

`("cosec" x)/(log(tan x/2))`

Integrate the following with respect to x :

`(sin 2x)/("a"^2 + "b"^2 sin^2x)`

Integrate the following with respect to x :

`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`