Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Advertisements
उत्तर
`int cosx/(cos(x - "a")) "d"x`
Put `x - "a"` = u
x = `"u" + "a"`
dx = du
`int cosx/(cos(x - "a")) "d"x = int (cos("u" + "a"))/(cos "u") "du"`
= `int (cos "u" cos "a" - sin "u" sin "a")/(cos "u") "du"`
= `int ((cos "u" cos "a")/(cos "u") - (sin"u" sin"a")/cos"u") "du"`
= `int cos "a" " du" - int tan "u" sin "a" * "du"`
= `cos "a" int "du" - sin "a" int tan "u" "du"`
= `cos "a"("u") - sin "a" log |sec "u"| + "c"`
`int cosx/(cos(x - "a")) "d"x = (x - "a") cos"a" - sin"a" log|sec(x - "a")| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
