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
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
`int(5x + 2)/(3x - 4) dx` = ______
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int sqrt(x^2 - a^2)/x dx` = ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1+ x + x^2/(2!)) dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
