Advertisements
Advertisements
Question
`int (1 + x)/(x + "e"^(-x)) "d"x`
Solution
Let I = `int (1 + x)/(x + "e"^(-x)) "d"x`
= `int (1 + x)/(x + 1/"e"^x) "d"x`
= `int (1 + x)/((x*"e"^x + 1)/("e"^x)) "d"x`
= `int ("e"^x (1 + x))/(x*"e"^x + 1) "d"x`
Put x. ex + 1 = t
∴ [x. (ex) + ex. (1) + 0] dx = dt
∴ ex (x + 1) dx = dt
∴ I = `int "dt"/"t"`
= log |t| + c
∴ I = log |x. ex + 1| + c
APPEARS IN
RELATED QUESTIONS
Evaluate : `∫1/(3+2sinx+cosx)dx`
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t.x:
cos8xcotx
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
`int dx/(1 + e^-x)` = ______
`int1/(4 + 3cos^2x)dx` = ______
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
Write `int cotx dx`.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
