Integrate the following functions with respect to x : 1+cos4xcosx-tanx

Integrate the following functions with respect to x :

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

बेरीज

`int (1 + cos 4x)/(cos x - tan x) * "d"x = int (1 + cos 2(2x))/(cosx/sinx - sinx/cosx) * "d"x`

= `int (2cos^2 2x)/((sin^2x - cos^2x)/(sinx cos x)) * "d"x`

= `int (2sin x ocs x * cos^2 2x)/(cos^2x - sin^2x) * "d"x`

= `int (2sinx cosx * cos^2 2x)/(cos^2x - sin^2x) * "d"x`

= `int (sin 2x cos^2x)/(cos 2x) * "d"x`

= `int sin 2x cos 2x * "d"x`

= `int 1/2 xx 2 sin 2x cos 2x * "d"x` .......[sin 2A = 2 sin A cos A]

= `1/2 int sin 4x * "d"x`

= `1/2 xx - (cos 4x)/4 + "c"`

= `- 1/8 cos 4x + "c"`

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पाठ 11: Integral Calculus - Exercise 11.5 [पृष्ठ २०२]

पाठ 11 Integral Calculus
Exercise 11.5 | Q 12 | पृष्ठ २०२

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

Integrate the following functions with respect to x :

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

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 :

`(sin^2x)/(1 + cosx)`

Integrate the following with respect to x :

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