Advertisements
Advertisements
Question
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Advertisements
Solution
`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
RELATED QUESTIONS
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
