Advertisements
Advertisements
Question
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Advertisements
Solution
`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"`
APPEARS IN
RELATED QUESTIONS
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
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 :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
x5ex2
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Choose the correct alternative:
`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
