Advertisements
Advertisements
प्रश्न
Integrate the functions:
`x/(e^(x^2))`
Advertisements
उत्तर
Let `I = int x/ (e^(x^(2))) dx`
Put x2 = t
⇒ 2x dx = dt
∴ `I = 1/2 int dt/e^t`
`= 1/2 int e^-t dt`
`= 1/2 (e^-t/-1) + C`
`= -1/(2e^t) + C`
`= -1/ 2^(e^(x^2)) + C`
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
`int (sin4x)/(cos 2x) "d"x`
`int (7x + 9)^13 "d"x` ______ + c
Evaluate `int(3x^2 - 5)^2 "d"x`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
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 ______.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
