Advertisements
Advertisements
Question
Integrate the following with respect to x :
`1/(x log x log (log x))`
Advertisements
Solution
`int 1/(x log x log (log x)) * "d"x`
Put `log(log x)` = u
`1/log x xx 1/x xx "d"x` = du
`1/(xlogx) "d"x` = du
`int 1/(log(log x)) * 1/(xlogx) "d"x = int 1/"u" * "du" + "c"`
= `log|"u"| + "c"`
`int 1/(log(log x)) * 1/(xlogx) "d"x = log |log(log x)| + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
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 "e"^(- 4x) cos "d"x` is
