Advertisements
Advertisements
प्रश्न
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Advertisements
उत्तर
Let I = `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Put aex − be−x = t
∴ `["ae"^("x") − "be"^(−"x") .(-1)] "dx" = "dt"`
∴ `("ae"^("x") + "be"^(−"x")) "dx" = "dt"`
∴ I = `int "dt"/"t"`
∴ I = `int 1/"t" "dt"`
∴ I = log | t | + c
∴ I = log | aex − be−x | + c
APPEARS IN
संबंधित प्रश्न
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
Integrate the function in x sin x.
Integrate the function in `x^2e^x`.
Integrate the function in x cos-1 x.
Integrate the function in x sec2 x.
`int e^x sec x (1 + tan x) dx` equals:
Evaluate the following : `int x^2.log x.dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^3 e^(x^2)`dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
`int 1/sqrt(2x^2 - 5) "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
∫ log x · (log x + 2) dx = ?
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
Find `int_0^1 x(tan^-1x) "d"x`
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
