Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Advertisements
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(tansqrtx)/sqrtxdx`
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/(9x^2 - 4)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
