Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
उत्तर
`int ("cosec" x)/(log(tan x/2)) "d"x`
Put `log (tan x/2)` = u
`1/(tan x/2) xx sec^2 x/2 xx 1/2 xx "d"x` = du
`cot x/2 xx 1/(cos^2 x/2) xx 1/2 xx "d"x` = du
`(cos x/2)/(sin x/2) xx 1/(cos^2 x/2) xx 1/2 xx "d"x` = du
`1/(2sin x/2 cos x/2) "d"x` = du
`1/sinx "d"x` = du
`"cosec" x "d"x` = du
∴ `int ("cosec" x)/(log(tan x/2)) "d"x = int "du"/"u"`
= `log |"u"| + "c"`
`int ("cosec" x)/(log(tan x/2)) "d"x = log |log(tan x/2)| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
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 :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/(25 - 4x^2)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
