Integrate the following functions with respect to x: x2-2x-3

Integrate the following functions with respect to x:

`sqrt(x^2 - 2x - 3)`

बेरीज

`int sqrt(x^2 - 2x - 3) "d"x = int sqrt((x - 1)^2 - 1^2 - 3) "d"x`

= `int sqrt((x - 1)^2 - 4) "d"x`

= `int sqrt((x - 1)^2 - 2^2) "d"x`

Put x – 1 = t

dx = dt

= `int sqrt("t"^2 - 2^2) "dt"`

= `"t"/2 sqrt("t"^2 - 2^2) - 2^2/2 log |"t" + sqrt("t"^2 - 2^2)| + "c"`

= `(x - 1)/2 sqrt((x - 1)^2 - 4) - 2 log|x - 1 + sqrt((x - 1)^2 - 4)| + "c"`

= `(x - 1)/2 sqrt(x^2 - 2x + 1 - 4) - 2 log|x - 1 sqrt(x^2 - 2x + 1 - 4) | + "c"`

`int sqrt(x^2 - 2x - 3) "d"x = (x - 1)/2 sqrt(x^2 - 2x - 3) - 2 log |x - 1 + sqrt(x^2 - 2x - 3)| + "c"`

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पाठ 11: Integral Calculus - Exercise 11.12 [पृष्ठ २२५]

पाठ 11 Integral Calculus
Exercise 11.12 | Q 1. (ii) | पृष्ठ २२५

Integrate the following functions with respect to x :

`(cos 2x)/(sin^2x cos^2x)`

Integrate the following functions with respect to x :

`(1 + cos 4x)/(cos x - tan x)`

Integrate the following functions with respect to x :

`(3x + 4) sqrt(3x + 7)`

Integrate the following functions with respect to x :

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

Integrate the following with respect to x :

`("e"^x - "e"^-x)/("e"^x + "e"^-x)`

Integrate the following with respect to x :

`(sin sqrt(x))/sqrt(x)`

Integrate the following with respect to x :

x(1 – x)¹⁷

Integrate the following with respect to x:

x sin 3x

Integrate the following with respect to x:

x log x

Integrate the following with respect to x:

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

Integrate the following functions with respect to x:

`sqrt(81 + (2x + 1)^2`

Integrate the following functions with respect to x:

`sqrt((x + 1)^2 - 4)`