Integrate the following with respect to x : eeeeex-e-xex+e-x

Integrate the following with respect to x :

`("e"^x - "e"^-x)/("e"^x + "e"^-x)`

Sum

`int ("e"^x - "e"^-x)/("e"^x + "e"^-x) * "d"x`

Put e^x + e^–x = u

(e^x – 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"`

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Chapter 11: Integral Calculus - Exercise 11.6 [Page 206]

Chapter 11 Integral Calculus
Exercise 11.6 | Q 3 | Page 206

Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.

Integrate the following functions with respect to x :

`[sqrt(x) + 1/sqrt(x)]^2`

Integrate the following functions with respect to x :

`"e"^(x log "a") "e"^x`

Integrate the following functions with respect to x :

`(x + 1)/((x + 2)(x + 3))`

Integrate the following with respect to x :

`(sin sqrt(x))/sqrt(x)`

Integrate the following with respect to x :

`("cosec" x)/(log(tan x/2))`

Integrate the following with respect to x :

`cosx/(cos(x - "a"))`

Integrate the following with respect to x:

x log x

Integrate the following with respect to x:

`tan^-1 ((8x)/(1 - 16x^2))`

Integrate the following with respect to x:

`"e"^("a"x) cos"b"x`

Find the integrals of the following:

`1/((x + 1)^2 - 25)`

Find the integrals of the following:

`1/sqrt((2 + x)^2 - 1)`

Find the integrals of the following:

`1/sqrt(x^2 - 4x + 5)`