Advertisements
Advertisements
Question
Integrate the following with respect to x :
`cot x/(log(sin x))`
Advertisements
Solution
`int cot x/(log(sin x)) "d"x`
Put `log(sin x)` = u
`1/sin x xx cos x "d"x` = du
`cosx/sinx * "d"x` = du
`cot x * "d"x` = du
`int cot x/(log(sin x)) "d"x = int "du"/"u"`
= `log |"u"| + "c"`
`int cot x/(log(sin x)) "d"x = log |log(sin x)| + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
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 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Integrate the following with respect to x:
`"e"^x sec x(1 + tan x)`
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/(6x - 7 - x^2)`
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
