Integrate the following with respect to x : sin-1x1-x2

Integrate the following with respect to x :

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

बेरीज

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

`sin^-1x` = u

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

`int (sin^-1x)/sqrt(1 - x^2) "d"x = int "u" * "du"`

= `"u"^2/2 + "c"`

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

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पाठ 11: Integral Calculus - Exercise 11.6 [पृष्ठ २०६]

पाठ 11 Integral Calculus
Exercise 11.6 | Q 9 | पृष्ठ २०६

Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx

Integrate the following functions with respect to x :

`[sqrt(x) + 1/sqrt(x)]^2`

Integrate the following functions with respect to x :

`(3 + 4cosx)/(sin^2x)`

Integrate the following functions with respect to x :

`1/(sqrt(x + 3) - sqrt(x - 4))`

Integrate the following with respect to x :

x(1 – x)¹⁷

Integrate the following with respect to x:

25xe^–5x

Integrate the following with respect to x:

x log x

Find the integrals of the following:

`1/sqrt(x^2 - 4x + 5)`

Integrate the following with respect to x:

`(2x - 3)/(x^2 + 4x - 12)`

Integrate the following with respect to x:

`(2x + 3)/sqrt(x^2 + 4x + 1)`