Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
उत्तर
`int ("e"^x - "e"^-x)/("e"^x + "e"^-x) * "d"x`
Put ex + e–x = u
(ex – e–x) = du
`int ("e"^x - "e"^-x)/("e"^x + "e"^-x) * "d"x = int "du"/"u"`
= `log |"u"| + "c"`
`int ("e"^x - "e"^-x)/("e"^x + "e"^-x) * "d"x = log |"e"^x + "e"^-x| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
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:
x log x
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/(9x^2 - 4)`
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)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
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)/sqrt(x^2 - 1) "d"x` is
