Advertisements
Advertisements
Question
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Advertisements
Solution
`int (cos 2x)/(sin^2x cos^2x) "d"x = int (cos^2x - sin^2alpha)/(sin^2x cos^2x) "d"x`
= `int ((cos^2x)/(sin^2x cos^2x) - (sin^2x)/(sin^2x cos^2x)) "d"x`
= `int (1/(sin^2x) - 1/(cos^2x)) "d"x`
= `int ("cosec"^2x - sec^2x) "d"x`
= `int "cosec"^2x "d"x - int sec^2x "d"x`
= `- cot x - tan x + "c"`
= `- [cosx/sinx + sinx/cosx] + "c"`
= `-[(cos^2x + sin^2x)/(sinx cosx)] + "c"`
= `- 2/(sin 2x) + "c"`
= – 2 cosec 2x + c
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
